ARRAY to MM

Description

Convert a 3-dimensional array [n, p, 2] to MM format (data.frame with paired _min/_max columns).

Usage

ARRAY_to_MM(data)

Arguments

Value

A data.frame with 2p columns (paired _min/_max).

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
mm <- ARRAY_to_MM(x)
mm

ARRAY to RSDA

Description

Convert a 3-dimensional array [n, p, 2] to RSDA format (symbolic_tbl with symbolic_interval columns).

Usage

ARRAY_to_RSDA(data)

Arguments

Value

A symbolic_tbl with p symbolic_interval columns.

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
rsda <- ARRAY_to_RSDA(x)
rsda

ARRAY to iGAP

Description

Convert a 3-dimensional array [n, p, 2] to iGAP format (data.frame with comma-separated interval values).

Usage

ARRAY_to_iGAP(data)

Arguments

Value

A data.frame in iGAP format with comma-separated "min,max" values.

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
igap <- ARRAY_to_iGAP(x)
igap

MM to ARRAY

Description

Convert MM format (paired _min/_max columns) to a 3-dimensional array [n, p, 2].

Usage

MM_to_ARRAY(data)

Arguments

Value

A numeric array of dimension [n, p, 2] with dimnames. Non-interval columns are excluded.

Examples

data(mushroom.int)
mm <- RSDA_to_MM(mushroom.int, RSDA = FALSE)
arr <- MM_to_ARRAY(mm)
dim(arr)

MM to RSDA

Description

To convert MM format interval dataframe to RSDA format (symbolic_tbl).

Usage

MM_to_RSDA(data)

Arguments

Value

Return a symbolic_tbl dataframe with complex-encoded interval columns.

Examples

data(mushroom.int)
mm <- RSDA_to_MM(mushroom.int, RSDA = FALSE)
rsda <- MM_to_RSDA(mm)

MM to iGAP

Description

To convert MM format to iGAP format.

Usage

MM_to_iGAP(data)

Arguments

Value

Return a dataframe with the iGAP format.

Examples

data(face.iGAP)
face <- iGAP_to_MM(face.iGAP, 1:6)
MM_to_iGAP(face)

RSDA Format

Description

This function changes the format of the data to conform to RSDA format.

Usage

RSDA_format(data, sym_type1 = NULL, location = NULL, sym_type2 = NULL, var = NULL)

Arguments

Value

Return a dataframe with a label added to the previous column of symbolic variable.

Examples

data("mushroom.int.mm")
mushroom.set <- set_variable_format(data = mushroom.int.mm, location = 8, var = "Species")
mushroom.tmp <- RSDA_format(data = mushroom.set, sym_type1 = c("I", "S"),
                            location = c(25, 31), sym_type2 = c("S", "I", "I"),
                            var = c("Species", "Stipe.Length_min", "Stipe.Thickness_min"))

RSDA to ARRAY

Description

Convert RSDA format (symbolic_tbl) to a 3-dimensional array [n, p, 2] where slice [,,1] contains the minima and slice [,,2] contains the maxima.

Usage

RSDA_to_ARRAY(data)

Arguments

Value

A numeric array of dimension [n, p, 2] with dimnames. Only interval (symbolic_interval) columns are included.

Examples

data(mushroom.int)
arr <- RSDA_to_ARRAY(mushroom.int)
dim(arr)  # [23, 3, 2]

RSDA to MM

Description

To convert RSDA format interval dataframe to MM format.

Usage

RSDA_to_MM(data, RSDA = TRUE)

Arguments

Value

Return a dataframe with the MM format.

Examples

data(mushroom.int)
RSDA_to_MM(mushroom.int, RSDA = FALSE)

RSDA to iGAP

Description

To convert RSDA format interval dataframe to iGAP format.

Usage

RSDA_to_iGAP(data)

Arguments

Value

Return a dataframe with the iGAP format.

Examples

data(mushroom.int)
RSDA_to_iGAP(mushroom.int)

SODAS to ARRAY

Description

Convert SODAS format (XML file) to a 3-dimensional array [n, p, 2].

Usage

SODAS_to_ARRAY(XMLPath)

Arguments

Value

A numeric array of dimension [n, p, 2] with dimnames.

Examples

## Not run: 
arr <- SODAS_to_ARRAY("C:/Users/user/AppData/abalone.xml")

## End(Not run)

SODAS to MM

Description

To convert SODAS format interval dataframe to the MM format.

Usage

SODAS_to_MM(XMLPath)

Arguments

Value

Return a dataframe with the MM format.

Examples

## Not run: 
# Read from a SODAS XML file:
abalone <- SODAS_to_MM("C:/Users/user/AppData/abalone.xml")

## End(Not run)

SODAS to iGAP

Description

To convert SODAS format interval dataframe to the iGAP format.

Usage

SODAS_to_iGAP(XMLPath)

Arguments

Value

Return a dataframe with the iGAP format.

Examples

## Not run: 
# Read from a SODAS XML file:
abalone <- SODAS_to_iGAP("C:/Users/user/AppData/abalone.xml")

## End(Not run)

Abalone Dataset (iGAP Format)

Description

Interval-valued dataset of 24 units from the UCI Abalone dataset, aggregated by sex and age group. iGAP format (comma-separated interval strings). See abalone.int for the Min-Max column format.

Usage

data(abalone.iGAP)

Format

A data frame with 24 observations (e.g., F-10-12, M-4-6) and 7 character columns in iGAP format (comma-separated "min, max" strings):

• Length: Shell length range.

• Diameter: Shell diameter range.

• Height: Shell height range.

• Whole: Whole weight range.

• Shucked: Shucked weight range.

• Viscera: Viscera weight range.

• Shell: Shell weight range.

Row names encode Sex-AgeGroup (e.g., F-10-12 = Female age 10–12).

Metadata

Source

UCI Machine Learning Repository.

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(abalone.iGAP)

Abalone Interval Dataset

Description

Interval-valued dataset of 24 units from the UCI Abalone dataset, aggregated by sex and age group. Min-Max column format (two columns per variable). See abalone.iGAP for the iGAP format version.

Usage

data(abalone.int)

Format

A data frame with 24 observations and 14 columns (7 interval variables in _min/_max pairs):

• Length_min, Length_max: Shell length range.

• Diameter_min, Diameter_max: Shell diameter range.

• Height_min, Height_max: Shell height range.

• Whole_min, Whole_max: Whole weight range.

• Shucked_min, Shucked_max: Shucked weight range.

• Viscera_min, Viscera_max: Viscera weight range.

• Shell_min, Shell_max: Shell weight range.

Row names encode Sex-AgeGroup (e.g., F-10-12 = Female age 10–12).

Metadata

Source

UCI Machine Learning Repository.

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(abalone.int)

Acid Rain Pollution Indices Interval Dataset

Description

Interval-valued acid rain pollution indices for sulphates and nitrates (kg/hectares) for 2 US states (Massachusetts and New York).

Usage

data(acid_rain.int)

Format

A data frame with 2 observations and 5 variables in Min-Max format:

• state: State name (character).

• sulphate_l, sulphate_u: Sulphate pollution index range (kg/hectares).

• nitrate_l, nitrate_u: Nitrate pollution index range (kg/hectares).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.21.

Examples

data(acid_rain.int)

Age-Cholesterol-Weight Interval Dataset

Description

Interval-valued dataset of 7 age-group observations with cholesterol and weight measurements. Each observation aggregates individuals in a 10-year age band with interval ranges for cholesterol and weight.

Usage

data(age_cholesterol_weight.int)

Format

A symbolic data frame (symbolic_tbl) with 7 observations and 4 variables:

• Age: Age range (years, interval).

• Cholesterol: Cholesterol level range (mg/dL, interval).

• Weight: Weight range (pounds, interval).

• n: Number of individuals in the age group (numeric).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(age_cholesterol_weight.int)

World Age Pyramids Histogram-Valued Dataset (2014)

Description

Histogram-valued dataset of 229 countries with 3 population age pyramid histograms (both sexes, male, female). Each histogram has 21 age bins representing the distribution of the population across age groups.

Usage

data(age_pyramids.hist)

Format

A data frame with 229 observations (countries) and 3 histogram-valued variables:

• Both.Sexes.Population: Histogram of total population by age group.

• Male.Population: Histogram of male population by age group.

• Female.Population: Histogram of female population by age group.

Row names are country names (e.g., WORLD, Afghanistan, Albania).

Metadata

Source

HistDAWass R package (Age_Pyramids_2014 dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: A new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (Age_Pyramids_2014).

Examples

data(age_pyramids.hist)

Aggregate Tabular Data to Symbolic Data

Description

Aggregate tabular numerical data (n by p) into interval-valued or histogram-valued symbolic data (K by p) based on a grouping mechanism.

Usage

aggregate_to_symbolic(x, type = "int", group_by = "kmeans",
  stratify_var = NULL, K = 5, interval = "range",
  quantile_probs = c(0.05, 0.95), bins = 10, nK = NULL)

Arguments

Details

The function aggregates classical tabular data into symbolic data by:

1. Partitioning observations into groups via group_by (clustering, resampling, or a categorical variable).

2. Within each group, summarizing each numeric variable as an interval (min/max or quantiles) or a histogram.

When stratify_var is provided, grouping and aggregation are performed within each level of the stratification variable. Label values are prefixed by the stratum name (e.g., "setosa.cluster_1").

For type = "hist", bin boundaries are computed from the global data range to ensure comparability across groups.

Non-numeric columns (other than those used for grouping or stratification) are silently excluded from aggregation.

Value

• For type = "int": a symbolic_tbl (RSDA format) with a label column followed by symbolic_interval columns for each numeric variable (K rows, 1 + p columns).

• For type = "hist": a MatH object (K rows by p columns of histogram-valued data).

Examples

# Group by a categorical variable -> interval data
res1 <- aggregate_to_symbolic(iris, type = "int", group_by = "Species")
res1

# K-means clustering -> interval data
res2 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "kmeans", K = 3)

# Quantile-based intervals
res3 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "kmeans", K = 3,
                               interval = "quantile",
                               quantile_probs = c(0.1, 0.9))

# Resampling -> interval data
set.seed(42)
res4 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "resampling", K = 5, nK = 30)

# Histogram aggregation
res5 <- aggregate_to_symbolic(iris, type = "hist",
                               group_by = "Species", bins = 5)

# Hierarchical clustering -> interval data
res6 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "hclust", K = 3)

# Stratified aggregation
res7 <- aggregate_to_symbolic(iris, type = "int",
                               group_by = "kmeans", K = 2,
                               stratify_var = "Species")

JFK Airport Airline Flights Histogram-Valued Dataset

Description

Histogram-valued dataset of 16 airlines flying into JFK Airport. Six variables (Flight Time, Taxi In, Arrival Delay, Taxi Out, Departure Delay, Weather Delay) recorded as frequency distributions. This is the wide (flat table) format; see airline_flights2.modal for the modal-valued version.

Usage

data(airline_flights.hist)

Format

A data frame with 16 observations (Airline1–Airline16) and 17 numeric columns representing 6 histogram variables in wide format:

• Flight Time(<120), Flight Time([120, 220]), Flight Time(>220): Flight time distribution (3 bins).

• Taxi In(<4), Taxi In([4, 10]), Taxi In(>10): Taxi-in time distribution (3 bins).

• Arrival Delay(<0), Arrival Delay([0, 60]), Arrival Delay(>60): Arrival delay distribution (3 bins).

• Taxi Out(<16), Taxi Out([16, 30]), Taxi Out(>30): Taxi-out time distribution (3 bins).

• Departure Delay(<0), Departure Delay([0, 60]), Departure Delay(>60): Departure delay distribution (3 bins).

• Weather Delay(No), Weather Delay(Yes): Weather delay distribution (2 bins).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.7.

Examples

data(airline_flights.hist)

JFK Airport Airline Flights Modal-Valued Dataset

Description

Modal-valued version of the airline flights dataset. See airline_flights.hist for the wide-format version.

Usage

data(airline_flights2.modal)

Format

A symbolic data frame (symbolic_tbl) with 16 observations and 6 modal-valued variables:

• FlightTime: Modal distribution over flight time bins.

• TaxiIn: Modal distribution over taxi-in time bins.

• ArrivalDelay: Modal distribution over arrival delay bins.

• TaxiOut: Modal distribution over taxi-out time bins.

• DepartureDelay: Modal distribution over departure delay bins.

• WeatherDelay: Modal distribution over weather delay bins.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.7.

Examples

data(airline_flights2.modal)

Bank Interest Rates AR Model Symbolic Dataset

Description

Symbolic dataset of autoregressive time series models for 4 banks. Each bank is described by AR model order, parameters, and whether parameters are known.

Usage

data(bank_rates)

Format

A data frame with 4 observations (Bank1–Bank4) and 6 variables:

• bank: Bank identifier (character).

• order: AR model order (numeric).

• phi1: First AR parameter (numeric; NA if unknown).

• phi2: Second AR parameter (numeric; NA if order < 2 or unknown).

• phi1_known: Whether phi1 is known (logical).

• phi2_known: Whether phi2 is known (logical; NA if order < 2).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.9.

Examples

data(bank_rates)

Baseball Teams Interval Dataset

Description

Interval-valued data for 19 baseball teams with aggregated player batting statistics and a pattern variable classifying team performance.

Usage

data(baseball.int)

Format

A symbolic data frame (symbolic_tbl) with 19 observations and 3 variables:

• At_Bats: Range of at-bats across players (interval).

• Hits: Range of hits across players (interval).

• Pattern: Team performance pattern code (character).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(baseball.int)

Bat Species Interval Dataset

Description

Interval-valued data for 21 bat species described by 4 morphological measurements. Benchmark dataset for matrix visualization.

Usage

data(bats.int)

Format

A data frame with 21 observations and 9 columns (4 interval variables in _l/_u Min-Max pairs, plus a label):

• species: Bat species name (character).

• head_l, head_u: Head length range (mm).

• tail_l, tail_u: Tail length range (mm).

• height_l, height_u: Ear height range (cm).

• forearm_l, forearm_u: Forearm length range (mm).

Details

Used to demonstrate color coding schemes, the HCT-R2E seriation algorithm, and distance measure comparisons (Gowda-Diday, Hausdorff, City-Block, L1, L2, etc.) for interval data.

Metadata

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(bats.int)

Bird Species Mixed Symbolic Dataset

Description

Interval-valued morphological measurements for 20 bird specimens. Despite the .mix suffix, this dataset contains only interval-valued variables (density and size).

Usage

data(bird.mix)

Format

A symbolic data frame (symbolic_tbl) with 20 observations and 2 variables:

• Density: Feather density range (interval).

• Size: Body size range (cm, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.5.

Examples

data(bird.mix)

Bird Color Taxonomy Histogram Dataset

Description

Mixed symbolic dataset of 20 bird observations with histogram-valued feather density and body size, categorical tone, and distribution-valued shade (fuzzy taxonomy). From Tables 6.9 and 6.14 of Billard and Diday (2007).

Usage

data(bird_color_taxonomy.hist)

Format

A data frame with 20 observations and 4 variables:

• density: Histogram-valued feather density (up to 4 bins).

• size: Histogram-valued body size (2-bin).

• tone: Categorical tone (dark/light).

• shade: Distribution-valued shade (purple/red/white/yellow with fuzzy weights).

Metadata

Source

Billard, L. and Diday, E. (2007), Tables 6.9/6.14.

References

Billard, L. and Diday, E. (2007). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Tables 6.9 and 6.14.

Examples

data(bird_color_taxonomy.hist)

Bird Species Mixed Symbolic Dataset

Description

Symbolic data for 3 bird species (Swallow, Ostrich, Penguin) with interval-valued size, categorical flying, and categorical migration. Foundational SDA example from 600 individual bird observations.

Usage

data(bird_species.mix)

Format

A data frame with 3 observations (Swallow, Ostrich, Penguin) and 5 variables:

• species: Species name (character).

• flying: Flying ability (Yes/No, character).

• size_l, size_u: Size range (cm, Min-Max pair).

• migration: Migratory behavior (TRUE/FALSE, logical).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 1.2, p.6.

Examples

data(bird_species.mix)

Bird Species Extended Mixed Symbolic Dataset

Description

Three bird species (Geese, Ostrich, Penguin) with interval-valued height, distribution-valued color, and categorical flying/migratory variables.

Usage

data(bird_species_extended.mix)

Format

A data frame with 3 observations and 6 variables:

• species: Species name (character).

• flying: Flying ability (Yes/No, character).

• height_l: Height lower bound (cm, numeric).

• height_u: Height upper bound (cm, numeric).

• color: Color distribution as weighted set string (e.g., "{white, 0.3; black, 0.7}").

• migratory: Migratory behavior (Yes/No, character).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.19.

Examples

data(bird_species_extended.mix)

Blood Test Histogram Dataset

Description

Histogram-valued blood test results for 14 gender-age groups (e.g., Female-20, Male-50). Each observation contains histograms for cholesterol, hemoglobin, and hematocrit, represented as multi-bin distributions.

Usage

data(blood.hist)

Format

A data frame with 14 observations and 3 histogram-valued variables:

• Cholesterol: Histogram of cholesterol levels (mg/dL).

• Hemoglobin: Histogram of hemoglobin levels (g/dL).

• Hematocrit: Histogram of hematocrit levels (%).

Metadata

Source

HistDAWass R package (BLOOD dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (BLOOD dataset).

Examples

data(blood.hist)

Blood Pressure Interval Dataset

Description

Interval-valued blood pressure and pulse rate measurements for 15 patient groups.

Usage

data(blood_pressure.int)

Format

A symbolic data frame (symbolic_tbl) with 15 observations and 3 interval-valued variables:

• Pulse_Rate: Pulse rate range (beats per minute, interval).

• Systolic_Pressure: Systolic blood pressure range (mmHg, interval).

• Diastolic_Pressure: Diastolic blood pressure range (mmHg, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(blood_pressure.int)

Car Models Interval Dataset

Description

Interval-valued data for 8 car brands with price and performance specifications. Each brand aggregates multiple models into interval ranges.

Usage

data(car.int)

Format

A symbolic data frame (symbolic_tbl) with 8 observations and 5 variables:

• Car: Car brand name (character).

• Price: Price range (thousands of currency units, interval).

• Max_Velocity: Maximum velocity range (km/h, interval).

• Accn_Time: Acceleration time range (seconds 0–100 km/h, interval).

• Cylinder_Capacity: Engine cylinder capacity range (cc, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(car.int)

Italian Car Models Interval Dataset

Description

Interval-valued specifications for 33 Italian car models, classified into 4 categories (Utilitaria, Berlina, Ammiraglia, Sportiva). An extended version of the classic cars interval dataset with 8 interval-valued variables including dimensions.

Usage

data(car_models.int)

Format

A data frame with 33 observations and 9 variables:

• price: Price range (currency units).

• engine_cc: Engine displacement range (cc).

• top_speed: Top speed range (km/h).

• acceleration: Acceleration range (seconds 0-100 km/h).

• wheelbase: Wheelbase range (cm).

• length: Length range (cm).

• width: Width range (cm).

• height: Height range (cm).

• class: Car category (Utilitaria, Berlina, Ammiraglia, Sportiva).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(car_models.int)

Cardiological Examination Interval Dataset

Description

Interval-valued data from cardiological examinations of 44 patients. Each patient is described by 5 interval-valued physiological measurements.

Usage

data(cardiological.int)

Format

A data frame with 44 observations and 5 interval-valued variables:

• pulse: Pulse rate range (beats per minute).

• systolic: Systolic blood pressure range (mmHg).

• diastolic: Diastolic blood pressure range (mmHg).

• arterial1: First arterial measurement range.

• arterial2: Second arterial measurement range.

Metadata

Source

Extracted from RSDA package (cardiologicalv2).

References

Rodriguez, O. (2000). Classification et modeles lineaires en analyse des donnees symboliques. Doctoral Thesis, Universite Paris IX-Dauphine.

Examples

data(cardiological.int)

Cars Interval Dataset

Description

Interval-valued data for 27 car models classified into four classes (Utilitarian, Berlina, Sportive, Luxury), described by Price, EngineCapacity, TopSpeed and Acceleration intervals.

Usage

data(cars.int)

Format

A symbolic data frame (symbolic_tbl) with 27 observations and 5 variables:

• Price: Price range (interval).

• EngCap: Engine capacity range (cc, interval).

• TopSpeed: Top speed range (km/h, interval).

• Acceleration: Acceleration range (seconds 0–100 km/h, interval).

• class: Car class (Utilitarian, Berlina, Sportive, Luxury; set-valued).

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

References

Duarte Silva, A.P., Brito, P., Filzmoser, P. and Dias, J.G. (2021). MAINT.Data: Modelling and Analysing Interval Data in R. R Journal, 13(2).

Examples

data(cars.int)

Census Mixed Symbolic Dataset

Description

Mixed symbolic dataset of 10 census regions combining 6 different symbolic variable types: histograms (age, home value), distributions (gender, tenure), a multi-valued set (fuel), and an interval (income).

Usage

data(census.mix)

Format

A symbolic data frame (symbolic_tbl) with 10 observations (regions) and 6 variables:

• age: Histogram-valued age distribution (12 age bins).

• home_value: Histogram-valued home value distribution (7 value bins, in $1000s).

• gender: Distribution over gender (male, female).

• fuel: Multi-valued set of fuel types used.

• tenure: Distribution over housing tenure (owner, renter, vacant).

• income: Interval-valued household income range ($1000s).

Row names are Region_1 through Region_10.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-23.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-23.

Examples

data(census.mix)

Chinese Climate Monthly Histogram Dataset

Description

Histogram-valued monthly climate data for 60 Chinese weather stations. Each station has 14 climate variables measured across 12 months (168 histogram columns total). Histograms are reduced to 10 decile bins from the original HistDAWass distributions.

Usage

data(china_climate_month.hist)

Format

A data frame with 60 observations (stations) and 168 histogram-valued variables. Variables follow the pattern variable_Month (e.g., mean.temp_Jan). The 14 climate variables are: mean pressure, mean temperature, mean max/min temperature, total precipitation, sunshine duration, mean cloud amount, mean relative humidity, snow days, dominant wind direction, mean wind speed, dominant wind frequency, extreme max/min temperature.

Metadata

Source

HistDAWass R package (China_Month dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (China_Month dataset).

Examples

data(china_climate_month.hist)

Chinese Climate Seasonal Histogram Dataset

Description

Histogram-valued seasonal climate data for 60 Chinese weather stations. Each station has 14 climate variables measured across 4 seasons (56 histogram columns total). Histograms are reduced to 10 decile bins from the original HistDAWass distributions.

Usage

data(china_climate_season.hist)

Format

A data frame with 60 observations (stations) and 56 histogram-valued variables. Variables follow the pattern variable_Season (e.g., mean.temp_Spring). The 14 climate variables are: mean pressure, mean temperature, mean max/min temperature, total precipitation, sunshine duration, mean cloud amount, mean relative humidity, snow days, dominant wind direction, mean wind speed, dominant wind frequency, extreme max/min temperature.

Metadata

Source

HistDAWass R package (China_Seas dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (China_Seas dataset).

Examples

data(china_climate_season.hist)

China Meteorological Stations Quarterly Temperature Interval Dataset

Description

Interval-valued temperature data (Celsius) for 60 Chinese meteorological stations observed over the four quarters of years 1974 to 1988. One outlier observation (YinChuan_1982) has been discarded.

Usage

data(china_temp.int)

Format

A symbolic data frame (symbolic_tbl) with 899 observations and 5 variables:

• Q1: Quarter 1 (Jan–Mar) temperature range (tenths of degrees Celsius, interval).

• Q2: Quarter 2 (Apr–Jun) temperature range (interval).

• Q3: Quarter 3 (Jul–Sep) temperature range (interval).

• Q4: Quarter 4 (Oct–Dec) temperature range (interval).

• GeoReg: Geographic region classification (factor).

Details

Originates from the Long-Term Instrumental Climatic Database of the People's Republic of China. Widely used in the SDA literature for demonstrating standardization, clustering, self-organizing maps, MLE and MANOVA.

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

References

Brito, P. and Duarte Silva, A.P. (2012). Modelling interval data with Normal and Skew-Normal distributions. J. Appl. Stat., 39(1), 3-20.

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(china_temp.int)

China Monthly Temperature Intervals (15 Stations)

Description

Interval-valued dataset of monthly temperature ranges for 15 weather stations in China. Each station has 12 monthly temperature intervals (minimum and maximum observed temperatures in degrees Celsius) and an elevation value in meters.

Usage

data(china_temp_monthly.int)

Format

A symbolic data frame (symbolic_tbl) with 15 observations (weather stations) and 13 variables:

• January, February, March, April, May, June, July, August, September, October, November, December: Interval-valued monthly temperature ranges (degrees Celsius).

• Elevation: Station elevation above sea level (numeric, meters).

Row names are station names (e.g., BoKeTu, Hailaer, LaSa).

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-9.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-9.

Examples

data(china_temp_monthly.int)

Cholesterol by Gender and Age Histogram-Valued Dataset

Description

Histogram-valued cholesterol distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of cholesterol levels.

Usage

data(cholesterol.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• cholesterol: Histogram-valued cholesterol distribution.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.5.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.5.

Examples

data(cholesterol.hist)

clean_colnames

Description

This function is used to clean up variable names to conform to the RSDA format.

Usage

clean_colnames(data)

Arguments

Value

Data after cleaning variable names.

Examples

data(mushroom.int.mm)
mushroom.clean <- clean_colnames(data = mushroom.int.mm)

County Income by Gender Histogram-Valued Dataset

Description

Histogram-valued dataset of 12 counties with gender-stratified income histograms and sample sizes. Each county has a male income histogram, a female income histogram, and the number of respondents in each group.

Usage

data(county_income_gender.hist)

Format

A data frame with 12 observations (counties) and 4 variables:

• male_income: Histogram of male household income (4 bins from $0 to $100k).

• female_income: Histogram of female household income (4 bins from $0 to $100k).

• n_males: Number of male respondents (numeric).

• n_females: Number of female respondents (numeric).

Row names are County_1 through County_12.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 6-16.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 6-16.

Examples

data(county_income_gender.hist)

Forest Cover Types Histogram-Valued Dataset

Description

Histogram-valued dataset of 7 forest cover types with 4 topographic histogram variables. Each histogram describes the distribution of a terrain feature across locations classified as that cover type.

Usage

data(cover_types.hist)

Format

A data frame with 7 observations (cover types) and 4 histogram-valued variables:

• elevation: Histogram of elevation values (meters).

• distance_to_water: Histogram of horizontal distance to nearest water source (meters).

• hillshade: Histogram of hillshade index values.

• slope: Histogram of slope values (degrees).

Row names are CoverType_1 through CoverType_7.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-21.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-21.

Examples

data(cover_types.hist)

Credit Card Expenses Interval Dataset

Description

Interval-valued credit card spending aggregated by person-month. Three individuals' (Jon, Tom, Leigh) monthly expenditures across five categories.

Usage

data(credit_card.int)

Format

A data frame with 6 observations and 11 columns (5 interval variables in _l/_u Min-Max pairs, plus a label):

• person_month: Person-month identifier (e.g., "Jon - January"; character).

• food_l, food_u: Food expenditure range (USD).

• social_l, social_u: Social expenditure range (USD).

• travel_l, travel_u: Travel expenditure range (USD).

• gas_l, gas_u: Gas expenditure range (USD).

• clothes_l, clothes_u: Clothes expenditure range (USD).

Details

The original classical dataset (Table 2.3) records individual transactions. The symbolic version (Table 2.4) aggregates into interval-valued observations for each person-month combination.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Tables 2.3-2.4.

Examples

data(credit_card.int)

Crime Demographics Dataset

Description

Modal-valued dataset of 15 gangs described by probability distributions over crime type, gender, and age group. This is the wide (flat table) format; see crime2.modal for the modal-valued version.

Usage

data(crime.modal)

Format

A data frame with 15 observations (gang1–gang15) and 7 numeric columns representing 3 modal variables in wide format:

• Crime(violent), Crime(non-violent), Crime(none): Distribution over crime types (3 bins).

• Gender(male), Gender(female): Distribution over gender (2 bins).

• Age(<20), Age(>=20): Distribution over age groups (2 bins).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(crime.modal)

Crime Demographics Modal-Valued Dataset

Description

Modal-valued version of the crime demographics dataset. See crime.modal for the wide-format version.

Usage

data(crime2.modal)

Format

A symbolic data frame (symbolic_tbl) with 15 observations and 3 modal-valued variables:

• Crime: Modal distribution over crime types (violent, non-violent, none).

• Gender: Modal distribution over gender (male, female).

• Age: Modal distribution over age groups (<20, >=20).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(crime2.modal)

WTI Crude Oil Futures Daily High/Low Interval Time Series

Description

Daily high and low prices of WTI (West Texas Intermediate) crude oil futures from January 2, 2003 to December 30, 2011 (2261 trading days). This dataset matches the period used by Yang, Han, Hong and Wang (2016) for analyzing crisis impacts on crude oil prices using interval time series modelling.

Usage

data(crude_oil_wti.its)

Format

A data frame with 2261 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price (USD per barrel).

• high: Daily high price (USD per barrel).

Details

WTI crude oil is a benchmark for oil prices in the Americas. This dataset covers a period that includes the 2003 Iraq War, the 2007–2008 oil price spike (reaching nearly USD 150/barrel), the 2008 global financial crisis, and the subsequent recovery. The wide variation in price levels and volatility regimes makes this dataset ideal for evaluating interval time series models under structural breaks.

Metadata

Source

Yahoo Finance, ticker CL=F. Downloaded via the quantmod package.

References

Yang, W., Han, A., Hong, Y. and Wang, S. (2016). Analysis of crisis impact on crude oil prices: A new approach with interval time series modelling. Quantitative Finance, 16(12), 1917–1928.

Examples

data(crude_oil_wti.its)
head(crude_oil_wti.its)
plot(crude_oil_wti.its$date, crude_oil_wti.its$high, type = "l",
     col = "red", ylab = "Price (USD/barrel)", xlab = "Date",
     main = "WTI Crude Oil Daily High/Low (2003-2011)")
lines(crude_oil_wti.its$date, crude_oil_wti.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Dow Jones Industrial Average Daily High/Low Interval Time Series

Description

Daily high and low prices of the Dow Jones Industrial Average (DJIA) from January 2, 2004 to December 30, 2005 (504 trading days). This dataset matches the period used in the foundational interval time series work by Arroyo, Gonzalez-Rivera and Mate (2011).

Usage

data(djia.its)

Format

A data frame with 504 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price of the DJIA.

• high: Daily high price of the DJIA.

Details

The DJIA is a price-weighted index of 30 prominent companies listed on stock exchanges in the United States. Each observation represents a trading day with the daily low and high prices forming an interval. This dataset has been used alongside the S&P 500 to compare interval forecasting methods.

Metadata

Source

Yahoo Finance, ticker ^DJI. Downloaded via the quantmod package.

References

Arroyo, J., Gonzalez-Rivera, G. and Mate, C. (2011). Forecasting with interval and histogram data: Some financial applications. In Handbook of Empirical Economics and Finance, pp. 247–280. Chapman and Hall/CRC.

Examples

data(djia.its)
head(djia.its)
plot(djia.its$date, djia.its$high, type = "l", col = "red",
     ylab = "Price", xlab = "Date", main = "DJIA Daily High/Low")
lines(djia.its$date, djia.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

E. coli Transport Routes Interval Dataset

Description

Interval-valued dataset of 9 E. coli transport routes with 5 interval variables representing biochemical pathway measurements.

Usage

data(ecoli_routes.int)

Format

A symbolic data frame (symbolic_tbl) with 9 observations (transport routes) and 5 interval-valued variables:

• Y1 through Y5: Interval-valued biochemical pathway measurements.

Row names are Route_1 through Route_9.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 8-10.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 8-10.

Examples

data(ecoli_routes.int)

European Employment by Gender and Age Interval Dataset

Description

Interval-valued proportions for 12 sex-age population groups across employment variables (employment type, education, industry sector, occupation, marital status). Used for factorial discriminant analysis.

Usage

data(employment.int)

Format

A data frame with 12 observations and 20 columns (9 interval variables in _l/_u Min-Max pairs, plus a group label and class):

• group: Sex-age group identifier (character).

• full_time_l, full_time_u: Full-time employment proportion range.

• part_time_l, part_time_u: Part-time employment proportion range.

• primary_studies_l, primary_studies_u: Primary studies proportion range.

• secondary_studies_l, secondary_studies_u: Secondary studies proportion range.

• uni_studies_l, uni_studies_u: University studies proportion range.

• employee_l, employee_u: Employee proportion range.

• manufacturing_l, manufacturing_u: Manufacturing sector proportion range.

• construction_l, construction_u: Construction sector proportion range.

• wholesale_retail_l, wholesale_retail_u: Wholesale/retail proportion range.

• class: Group classification (numeric).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 18.1.

Examples

data(employment.int)

US Energy Consumption Distribution-Valued Dataset

Description

Distribution-valued dataset of energy consumption across US states. Each energy type described by Normal distribution parameters (mean, SD).

Usage

data(energy_consumption.distr)

Format

A data frame with 5 observations and 3 variables:

• type: Energy type.

• mean: Mean consumption across 50 states.

• sd: Standard deviation.

Details

Five types: Petroleum, Natural Gas, Coal, Hydroelectric, Nuclear Power. Values are rescaled consumption from the US Census Bureau (2004).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.8.

Examples

data(energy_consumption.distr)

Energy Usage Distribution-Valued Dataset

Description

Distribution-valued dataset for 10 towns (geographic areas) with categorical probability distributions for fuel type and central heating. Each observation has two distribution-valued variables.

Usage

data(energy_usage.distr)

Format

A data frame with 10 observations and 2 distribution-valued variables:

• fuel_type: Distribution over fuel types (None, Gas, Oil, Electricity, Coal).

• central_heating: Distribution over central heating (No, Yes).

Row names are Town_1 through Town_10.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 3.7.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 3.7.

Examples

data(energy_usage.distr)

EPA Environmental Data Mixed Symbolic Dataset

Description

Mixed symbolic dataset from the US EPA with 14 state-group observations and 17 variables of mixed types: interval-valued environmental measurements and modal-valued (distributional) categorical variables.

Usage

data(environment.mix)

Format

A symbolic data frame (symbolic_tbl) with 14 observations and 17 variables:

• URBANICITY: Modal-valued urbanicity distribution (character).

• INCOMELEVEL: Modal-valued income level distribution (character).

• EDUCATION: Modal-valued education distribution (character).

• REGIONDEVELOPME: Modal-valued regional development distribution (character).

• CONTROL: Environmental control index range (interval).

• SATISFY: Satisfaction index range (interval).

• INDIVIDUAL: Individual concern index range (interval).

• WELFARE: Welfare index range (interval).

• HUMAN: Human impact index range (interval).

• POLITICS: Political concern index range (interval).

• BURDEN: Burden index range (interval).

• NOISE: Noise pollution index range (interval).

• NATURE: Nature preservation index range (interval).

• SEASETC: Seas/coastal index range (interval).

• MULTI: Multi-indicator range (interval).

• WATERWASTE: Water/waste index range (interval).

• VEHICLE: Vehicle emissions index range (interval).

Metadata

Source

Extracted from ggESDA package (Environment).

References

Sun, Y. and Billard, L. (2020). Symbolic data analysis with the ggESDA package. Journal of Statistical Software.

Examples

data(environment.mix)

Euro/Dollar Exchange Rate Daily High/Low Interval Time Series

Description

Daily high and low values of the EUR/USD exchange rate from January 1, 2004 to December 30, 2005 (520 trading days). Inspired by the dataset used by Arroyo, Espinola and Mate (2011) for exponential smoothing methods for interval time series.

Usage

data(euro_usd.its)

Format

A data frame with 520 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low EUR/USD exchange rate.

• high: Daily high EUR/USD exchange rate.

Details

The EUR/USD exchange rate is the most traded currency pair in the world foreign exchange market. Each observation represents a trading day with the daily low and high exchange rates (USD per EUR) forming an interval. Note: the original study by Arroyo et al. (2011) used the period 2002–2003 (519 trading days); this dataset covers 2004–2005 because Yahoo Finance historical data for this ticker is only available from late 2003 onward.

Metadata

Source

Yahoo Finance, ticker EURUSD=X. Downloaded via the quantmod package.

References

Arroyo, J., Espinola, R. and Mate, C. (2011). Different approaches to forecast interval time series: A comparison in finance. Computational Economics, 37(2), 169–191.

Examples

data(euro_usd.its)
head(euro_usd.its)
plot(euro_usd.its$date, euro_usd.its$high, type = "l", col = "red",
     ylab = "EUR/USD", xlab = "Date",
     main = "EUR/USD Daily High/Low (2004-2005)")
lines(euro_usd.its$date, euro_usd.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Exchange Rate Returns Histogram Time Series

Description

Histogram-valued time series of 108 monthly observations of daily exchange rate returns. Each observation is a histogram distribution of intra-month daily returns.

Usage

data(exchange_rate_returns.hist)

Format

A data frame with 108 observations and 1 histogram-valued variable:

• returns: Histogram of daily exchange rate returns within each month.

Metadata

Source

HistDAWass R package (RetHTS dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (RetHTS dataset).

Examples

data(exchange_rate_returns.hist)

Face Dataset (iGAP Format)

Description

Interval-valued facial measurement data for 27 face images (9 individuals x 3 replications) in iGAP format (comma-separated interval strings). Contains 6 distance measurements between facial landmarks.

Usage

data(face.iGAP)

Format

A data frame with 27 observations and 6 character columns in iGAP format (comma-separated "min,max" strings):

• AD: Distance AD (facial landmark pair).

• BC: Distance BC (facial landmark pair).

• AH: Distance AH (facial landmark pair).

• DH: Distance DH (facial landmark pair).

• EH: Distance EH (facial landmark pair).

• GH: Distance GH (facial landmark pair).

Row names encode individual and replication (e.g., FRA1, FRA2, FRA3).

Metadata

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(face.iGAP)

Finance Sector Interval Dataset

Description

Interval-valued data for 14 business sectors described by job-related financial variables (job cost codes, activity codes, budgets). Used for PCA demonstrations.

Usage

data(finance.int)

Format

A symbolic data frame (symbolic_tbl) with 14 observations and 7 variables:

• Sector: Business sector name (character).

• Job_Cost: Job cost range (currency units, interval).

• Job_Code: Job code range (interval).

• Activity_Code: Activity code range (interval).

• Monthly_Cost: Monthly cost range (currency units, interval).

• Annual_Budget: Annual budget range (currency units, interval).

• n: Number of entities in the sector (numeric).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 5.2.

Examples

data(finance.int)

Airline Flights Detailed Histogram-Valued Dataset

Description

Histogram-valued dataset of 16 airlines with 5 flight performance histograms. Each histogram has 12 bins describing the distribution of a performance metric across flights for that airline.

Usage

data(flights_detail.hist)

Format

A data frame with 16 observations (airlines) and 5 histogram-valued variables:

• airtime: Histogram of air time (minutes).

• taxi_in: Histogram of taxi-in time (minutes).

• arrival_delay: Histogram of arrival delay (minutes).

• taxi_out: Histogram of taxi-out time (minutes).

• departure_delay: Histogram of departure delay (minutes).

Row names are Airline_1 through Airline_16.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 5-1.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 5-1.

Examples

data(flights_detail.hist)

French Agriculture Histogram-Valued Dataset

Description

Histogram-valued dataset of 22 French regions with 4 economic histogram variables related to agricultural production. Each histogram describes the distribution of farm-level values within a region.

Usage

data(french_agriculture.hist)

Format

A data frame with 22 observations (French regions) and 4 histogram-valued variables:

• Y_TSC: Histogram of total standard coefficient.

• X_Wheat: Histogram of wheat production.

• X_Pig: Histogram of pig production.

• X_Cmilk: Histogram of cow milk production.

Row names are French region names (e.g., Ile-de-France, Picardie).

Metadata

Source

HistDAWass R package (Agronomique dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: A new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (Agronomique dataset).

Examples

data(french_agriculture.hist)

Freshwater Fish Heavy Metal Bioaccumulation Interval Dataset

Description

Interval-valued dataset of heavy metal concentrations in organs and tissues of 12 freshwater fish species, grouped into 4 feeding categories (Carnivores, Omnivores, Detritivores, Herbivores). Contains 13 interval-valued variables measuring metal concentrations in organs and organ-to-muscle ratios.

Usage

data(freshwater_fish.int)

Format

A data frame with 12 observations and 14 variables:

• body_length: Body length (cm).

• body_weight: Body weight (g).

• muscle: Metal concentration in muscle tissue.

• intestine: Metal concentration in intestine.

• stomach: Metal concentration in stomach.

• gills: Metal concentration in gills.

• liver: Metal concentration in liver.

• kidney: Metal concentration in kidney.

• liver_muscle_ratio: Liver-to-muscle concentration ratio.

• kidney_muscle_ratio: Kidney-to-muscle concentration ratio.

• gills_muscle_ratio: Gills-to-muscle concentration ratio.

• intestine_muscle_ratio: Intestine-to-muscle concentration ratio.

• stomach_muscle_ratio: Stomach-to-muscle concentration ratio.

• class: Feeding category (Carnivores, Omnivores, Detritivores, Herbivores).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(freshwater_fish.int)

Fuel Consumption by Region Dataset

Description

Modal-valued dataset describing fuel consumption patterns across 10 regions by proportions of heating fuel types (gas, oil, electricity, other) and per-capita expenditure.

Usage

data(fuel_consumption.modal)

Format

A symbolic data frame (symbolic_tbl) with 10 observations and 3 variables:

• Region: Region identifier (character).

• Expenditure: Per-capita fuel expenditure (numeric).

• Fuel_Type: Modal distribution over fuel types (gas, oil, electric, other).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 3.7.

Examples

data(fuel_consumption.modal)

Fungi Morphological Measurements Interval Dataset

Description

Interval-valued morphological measurements for 55 fungi specimens from 3 genera (Amanita, Agaricus, Boletus). Contains 5 interval-valued variables describing pileus and stipe dimensions and spore characteristics.

Usage

data(fungi.int)

Format

A data frame with 55 observations and 6 variables:

• pileus_width: Width of the pileus (cap).

• stipe_width: Width of the stipe (stem).

• stipe_thickness: Thickness of the stipe.

• spore_height: Height of the spores.

• spore_width: Width of the spores.

• class: Fungus genus (Amanita, Agaricus, Boletus).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(fungi.int)

Genome Dinucleotide Abundance Intervals

Description

Interval-valued dataset of dinucleotide relative abundances for 14 genome classes. Each class aggregates multiple genomes; the intervals represent the range of observed abundance values within each class for 10 dinucleotide pairs, plus a count variable.

Usage

data(genome_abundances.int)

Format

A symbolic data frame (symbolic_tbl) with 14 observations (genome classes) and 11 variables:

• CG: Interval-valued CG dinucleotide relative abundance.

• GC: Interval-valued GC dinucleotide relative abundance.

• TA: Interval-valued TA dinucleotide relative abundance.

• AT: Interval-valued AT dinucleotide relative abundance.

• CC: Interval-valued CC dinucleotide relative abundance.

• AA: Interval-valued AA dinucleotide relative abundance.

• AC: Interval-valued AC dinucleotide relative abundance.

• AG: Interval-valued AG dinucleotide relative abundance.

• CA: Interval-valued CA dinucleotide relative abundance.

• GA: Interval-valued GA dinucleotide relative abundance.

• n: Number of genomes in the class (integer).

Row names are Class_1 through Class_14.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 3-16.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 3-16.

Examples

data(genome_abundances.int)

Blood Glucose Histogram-Valued Dataset

Description

Histogram-valued dataset of 4 regions with a single histogram-valued variable describing the distribution of blood glucose measurements.

Usage

data(glucose.hist)

Format

A data frame with 4 observations (regions) and 1 histogram-valued variable:

• glucose: Histogram of blood glucose levels.

Row names are Region_1 through Region_4.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 4-14.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 4-14.

Examples

data(glucose.hist)

Hardwood Tree Species Histogram-Valued Dataset

Description

Histogram-valued climate data for 5 hardwood tree species in the southeastern United States. Each observation represents a species with 4 histogram-valued climate variables.

Usage

data(hardwood.hist)

Format

A data frame with 5 observations and 4 histogram-valued variables:

• ANNT: Annual temperature histogram (degrees C).

• JULT: July temperature histogram (degrees C).

• ANNP: Annual precipitation histogram (mm).

• MITM: Moisture index histogram.

Metadata

Source

Extracted from RSDA package (hardwoodBrito).

References

Brito, P. (2007). Modelling and Analysing Interval Data. In V. Esposito Vinzi et al. (Eds.), New Developments in Classification and Data Analysis, pp. 197-208. Springer.

Examples

data(hardwood.hist)

Human Development Index and Gender Indicators Interval Dataset

Description

Interval-valued World Bank gender indicators for 183 countries, with ordinal HDI classification. Contains interval ranges for Women, Business and the Law Index Score and proportion of seats held by women in national parliaments.

Usage

data(hdi_gender.int)

Format

A data frame with 183 observations and 6 variables:

• code: ISO 3166-1 alpha-3 country code.

• country: Country name.

• hdi: Human Development Index value (UNDP).

• women_law_index: Women, Business and the Law Index Score range.

• women_parliament: Proportion of seats held by women in national parliaments range (%).

• hdi_category: Ordered factor with HDI classification (Low < Medium < High < Very High).

Metadata

Source

https://github.com/aleixalcacer/OCFIVD

References

Alcacer, A., Barrel, A., Groenen, P. J. F. and Grana, M. (2023). Ordinal classification for interval-valued data and ordinal data. Expert Systems with Applications, 238, 121825.

Examples

data(hdi_gender.int)

Health Insurance Mixed Symbolic Dataset

Description

Classical (microdata) health insurance dataset of 51 individual patient records with 30 variables including demographics, clinical measurements, and diagnostic indicators. This is the raw data underlying the symbolic health_insurance2.modal dataset.

Usage

data(health_insurance.mix)

Format

A data frame with 51 observations and 30 variables (Y1–Y30):

• Y1: City (character).

• Y2: Gender (M/F, character).

• Y3: Age (integer).

• Y4: Sex (M/D, character).

• Y5: Marital status (S/M, character).

• Y6: Number of dependents (integer).

• Y7: Parents alive indicator (integer).

• Y8: Number of children (integer).

• Y9: Height (cm, integer).

• Y10: Weight (pounds, integer).

• Y11: Systolic blood pressure (mmHg, integer).

• Y12: Diastolic blood pressure (mmHg, integer).

• Y13: Cholesterol (mg/dL, integer).

• Y14: Cholesterol measure 2 (integer).

• Y15: Additional lab measurement (integer).

• Y16: Ratio measurement (numeric).

• Y17: Lab value (integer).

• Y18: Lab value (integer).

• Y19: Lab value (integer).

• Y20: Lab ratio (numeric).

• Y21: Additional lab value (integer).

• Y22: Additional lab value (integer).

• Y23: Blood chemistry value (numeric).

• Y24: Blood chemistry value (numeric).

• Y25: Blood chemistry value (numeric).

• Y26: Blood chemistry value (numeric).

• Y27: Blood chemistry value (numeric).

• Y28: Diagnostic indicator (Y/N, character).

• Y29: Diagnostic indicator (Y/N, character).

• Y30: Count variable (integer).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Tables 2.1-2.2.

Examples

data(health_insurance.mix)

Health Insurance Modal-Valued Dataset

Description

Modal-valued symbolic version of the health insurance dataset, aggregated into 6 disease-type-by-gender groups. See health_insurance.mix for the underlying microdata.

Usage

data(health_insurance2.modal)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 6 variables:

• Type Gender: Disease type and gender label (character).

• Age: Modal distribution over age bins.

• Marital Status: Modal distribution over marital status (M, S).

• Parents Alive: Modal distribution over number of parents alive (0, 1, 2).

• Weight: Modal distribution over weight bins (pounds).

• Cholesterol: Modal distribution over cholesterol bins (mg/dL).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.2b.

Examples

data(health_insurance2.modal)

Hematocrit by Gender and Age Histogram-Valued Dataset

Description

Histogram-valued hematocrit distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of hematocrit percentages.

Usage

data(hematocrit.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• hematocrit: Histogram-valued hematocrit distribution (%).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.14.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.14.

Examples

data(hematocrit.hist)

Hematocrit and Hemoglobin Bivariate Histogram-Valued Dataset

Description

Bivariate histogram-valued dataset with 10 observations, each described by a 2-bin hematocrit histogram and a 2-bin hemoglobin histogram. Used for bivariate symbolic regression demonstrations.

Usage

data(hematocrit_hemoglobin.hist)

Format

A data frame with 10 observations and 2 histogram-valued variables:

• hematocrit: Histogram-valued hematocrit distribution (%).

• hemoglobin: Histogram-valued hemoglobin distribution (g/dL).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 6.8.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 6.8.

Examples

data(hematocrit_hemoglobin.hist)

Hemoglobin by Gender and Age Histogram-Valued Dataset

Description

Histogram-valued hemoglobin distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of hemoglobin levels (g/dL).

Usage

data(hemoglobin.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• hemoglobin: Histogram-valued hemoglobin distribution (g/dL).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.6.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.6.

Examples

data(hemoglobin.hist)

Hierarchy Dataset

Description

Classical (microdata) dataset of 20 observations illustrating hierarchical categorical structures with a response variable Y and hierarchical predictors X1–X5. See hierarchy.int for the interval-valued version.

Usage

data(hierarchy)

Format

A data frame with 20 observations and 6 variables:

• Y: Response variable (numeric).

• X1: Hierarchy level 1 category (a/b/c, character).

• X2: Hierarchy level 2 category (a1/a2, character; NA for non-a).

• X3: Hierarchy level 3 category (a11/a12, character; NA for non-a1).

• X4: Numeric predictor for group b (numeric; NA for non-b).

• X5: Numeric predictor for group c (numeric; NA for non-c).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.15.

Examples

data(hierarchy)

Hierarchical Symbolic Dataset with Mixed Types

Description

Mixed symbolic dataset of 10 observations with hierarchical categorical variables, conditional histogram variables, and an interval-valued variable. From Table 6.20 of Billard and Diday (2007).

Usage

data(hierarchy.hist)

Format

A symbolic data frame (symbolic_tbl) with 10 observations and 7 variables:

• duration_time: Histogram-valued duration (2-bin).

• hierarchy_1: Categorical hierarchy level 1 (a/b/c).

• hierarchy_2: Categorical hierarchy level 2 (a1/a2), conditional on hierarchy_1 = a.

• hierarchy_3: Categorical hierarchy level 3 (a11/a12), conditional on hierarchy_2 = a1.

• glucose: Histogram-valued glucose (2-bin), conditional.

• pulse_rate: Histogram-valued pulse rate (2-bin), conditional.

• cholesterol: Interval-valued cholesterol level.

Metadata

Source

Billard, L. and Diday, E. (2007), Table 6.20.

References

Billard, L. and Diday, E. (2007). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 6.20.

Examples

data(hierarchy.hist)

Hierarchy Interval Dataset

Description

Interval-valued version of the hierarchy dataset. See hierarchy for the classical version.

Usage

data(hierarchy.int)

Format

A symbolic data frame (symbolic_tbl) with 20 observations and 6 variables:

• Y: Response variable range (interval).

• X1: Hierarchy level 1 category (a/b/c, character).

• X2: Hierarchy level 2 category (a1/a2, character; NA for non-a).

• X3: Hierarchy level 3 category (a11/a12, character; NA for non-a1).

• X4: Predictor range for group b (interval; NA for non-b).

• X5: Predictor range for group c (interval; NA for non-c).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.15.

Examples

data(hierarchy.int)

Statistics for Histogram Data

Description

Functions to compute the mean, variance, covariance, and correlation of histogram-valued data.

Usage

hist_mean(x, var_name, method = "BG", ...)

hist_var(x, var_name, method = "BG", ...)

hist_cov(x, var_name1, var_name2, method = "BG", ...)

hist_cor(x, var_name1, var_name2, method = "BG", ...)

Arguments

Details

Four functions are provided:

• hist_mean: Compute the mean of histogram-valued data.

• hist_var: Compute the variance of histogram-valued data.

• hist_cov: Compute the covariance between two histogram-valued variables.

• hist_cor: Compute the correlation between two histogram-valued variables.

Four methods are supported for all functions:

BG

Bertrand and Goupil (2000) method. Uses histogram bin boundaries and probabilities to compute first and second moments.

BD

Billard and Diday (2006) method. A signed decomposition using the sign of each bin's midpoint deviation from the overall mean and a quadratic form on the bin boundaries.

B

Billard (2008) method. Uses cross-products of deviations of the bin boundaries from the overall mean.

L2W

L2 Wasserstein method. Uses optimal-transport (Wasserstein) distances between the quantile functions of the histogram distributions.

For the mean, BG, BD, and B return the same value because they share the same first-order moment definition; only L2W uses a different (quantile-based) mean. For variance, covariance, and correlation, all four methods generally produce different results.

For hist_cor, the BG, BD, and B correlations all use the Bertrand-Goupil standard deviation S(Y) in the denominator, following Irpino and Verde (2015, Eqs. 30–32). Only the L2W method uses its own Wasserstein-based standard deviation in the denominator.

Value

A numeric value or vector for hist_mean and hist_var; a single numeric value for hist_cov and hist_cor.

Author(s)

Po-Wei Chen, Han-Ming Wu

See Also

int_mean int_var int_cov int_cor

Examples

library(HistDAWass)
x <- HistDAWass::BLOOD
hist_mean(x, var_name = "Cholesterol", method = "BG")
hist_mean(x, var_name = "Cholesterol", method = "BD")
hist_var(x, var_name = "Cholesterol", method = "BG")
hist_var(x, var_name = "Cholesterol", method = "BD")
hist_cov(x, var_name1 = "Cholesterol", var_name2 = "Hemoglobin", method = "BG")
hist_cor(x, var_name1 = "Cholesterol", var_name2 = "Hemoglobin", method = "BG")

Horse Breeds Interval Dataset

Description

Interval-valued data for 8 horse breeds (CES, CMA, PEN, TES, CEN, LES, PES, PAM) described by 6 variables: minimum/maximum weight, minimum/maximum height, cost of mares, cost of fillies.

Usage

data(horses.int)

Format

A symbolic data frame (symbolic_tbl) with 8 observations and 7 variables:

• Breed: Horse breed code (CES, CMA, PEN, TES, CEN, LES, PES, PAM; character).

• Minimum_Weight: Minimum weight range (kg, interval).

• Maximum_Weight: Maximum weight range (kg, interval).

• Minimum_Height: Minimum height range (cm, interval).

• Maximum_Height: Maximum height range (cm, interval).

• Mares_Cost: Cost of mares range (currency units, interval).

• Fillies_Cost: Cost of fillies range (currency units, interval).

Details

Extensively used in SDA for demonstrating divisive clustering, distance computation, hierarchy/pyramid construction, and complete objects.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 7.14.

Examples

data(horses.int)

Hospital Costs Histogram-Valued Dataset

Description

Histogram-valued cost distributions for 15 hospitals. Each observation is a hospital with a 10-bin histogram of patient costs.

Usage

data(hospital.hist)

Format

A data frame with 15 observations and 1 histogram-valued variable:

• cost: Histogram-valued cost distribution (currency units).

Row names are H1 through H15.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 3.12.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 3.12.

Examples

data(hospital.hist)

Household Characteristics Distribution-Valued Dataset

Description

Distribution-valued dataset of 12 counties with 3 categorical probability distribution variables describing household fuel type, number of rooms, and household income brackets.

Usage

data(household_characteristics.distr)

Format

A data frame with 12 observations (counties) and 3 distribution-valued variables:

• fuel_type: Distribution over fuel types (gas, electric, oil, wood, none).

• rooms: Distribution over room counts ({1,2}, {3,4,5}, {>=6}).

• household_income: Distribution over income brackets (<10, [10,25), [25,50), [50,75), [75,100), [100,150), [150,200), >=200).

Row names are County_1 through County_12.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 6-1.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 6-1.

Examples

data(household_characteristics.distr)

iGAP to ARRAY

Description

Convert iGAP format to a 3-dimensional array [n, p, 2].

Usage

iGAP_to_ARRAY(data, location = NULL)

Arguments

Value

A numeric array of dimension [n, p, 2] with dimnames.

Examples

data(abalone.iGAP)
arr <- iGAP_to_ARRAY(abalone.iGAP, 1:7)
dim(arr)

iGAP to MM

Description

To convert iGAP format to MM format.

Usage

iGAP_to_MM(data, location = NULL)

Arguments

Value

Return a dataframe with the MM format.

Examples

data(abalone.iGAP)
abalone <- iGAP_to_MM(abalone.iGAP, 1:7)

iGAP to RSDA

Description

To convert iGAP format interval dataframe to RSDA format (symbolic_tbl).

Usage

iGAP_to_RSDA(data, location = NULL)

Arguments

Value

Return a symbolic_tbl dataframe with complex-encoded interval columns.

Examples

data(abalone.iGAP)
rsda <- iGAP_to_RSDA(abalone.iGAP, 1:7)

IBOVESPA Daily High/Low Interval Time Series

Description

Daily high and low values of the Brazilian IBOVESPA stock market index from January 3, 2000 to December 28, 2012 (3216 trading days). This dataset matches the period used by Maciel, Ballini and Gomide (2016) for evolving granular analytics for interval time series forecasting.

Usage

data(ibovespa.its)

Format

A data frame with 3216 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low value of the IBOVESPA index.

• high: Daily high value of the IBOVESPA index.

Details

The IBOVESPA (Indice Bovespa) is the benchmark index of the Brazilian stock exchange (B3, formerly BM&FBOVESPA). It tracks the performance of the most actively traded stocks on the Sao Paulo stock exchange. The 13-year span of this dataset covers multiple market regimes including the 2008 global financial crisis, making it suitable for evaluating forecasting models under diverse conditions.

Metadata

Source

Yahoo Finance, ticker ^BVSP. Downloaded via the quantmod package.

References

Maciel, L., Ballini, R. and Gomide, F. (2016). Evolving granular analytics for interval time series forecasting. Granular Computing, 1(4), 213–224.

Examples

data(ibovespa.its)
head(ibovespa.its)
plot(ibovespa.its$date, ibovespa.its$high, type = "l", col = "red",
     ylab = "Index Value", xlab = "Date",
     main = "IBOVESPA Daily High/Low (2000-2012)")
lines(ibovespa.its$date, ibovespa.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Convert Interval Data Format

Description

Automatically detect the format of interval data and convert it to the target format.

Usage

int_convert_format(x, to = "MM", from = NULL, ...)

Arguments

Details

This function provides a unified interface for all interval format conversions. It automatically detects the source format (unless specified) and applies the appropriate conversion function.

Supported conversions:

• RSDA ??? MM, iGAP, ARRAY

• MM ??? iGAP, RSDA, ARRAY

• iGAP ??? MM, RSDA, ARRAY

• ARRAY ??? RSDA, MM, iGAP

• SODAS ??? MM, iGAP, ARRAY

Value

Interval data in the target format

Author(s)

Han-Ming Wu

See Also

int_detect_format int_list_conversions RSDA_to_MM RSDA_to_ARRAY MM_to_RSDA MM_to_ARRAY ARRAY_to_RSDA ARRAY_to_MM ARRAY_to_iGAP iGAP_to_MM iGAP_to_RSDA iGAP_to_ARRAY MM_to_iGAP

Examples

# Auto-detect and convert to MM
data(mushroom.int)
data_mm <- int_convert_format(mushroom.int, to = "MM")

# Explicitly specify source format
data(abalone.iGAP)
data_mm <- int_convert_format(abalone.iGAP, from = "iGAP", to = "MM")

# Convert MM to iGAP
data_igap <- int_convert_format(data_mm, to = "iGAP")

 # Convert multiple datasets to MM
datasets <- list(mushroom.int, abalone.int, car.int)
mm_datasets <- lapply(datasets, int_convert_format, to = "MM")

# Check what conversions are available
int_list_conversions()

Detect Interval Data Format

Description

Automatically detect the format of interval data.

Usage

int_detect_format(x)

Arguments

Details

Detection rules:

• RSDA: has class "symbolic_tbl" and contains complex columns

• MM: data.frame with paired "_min" and "_max" columns

• iGAP: data.frame with columns containing comma-separated values (e.g., "1.2,3.4")

• ARRAY: a 3-dimensional array with dim[3] = 2 (min/max slices)

• SODAS: character string ending with ".xml" (file path)

• SDS: alias for SODAS

Value

A character string indicating the detected format: "RSDA", "MM", "iGAP", "ARRAY", "SODAS", or "unknown"

Examples

data(mushroom.int)
int_detect_format(mushroom.int)  # Should return "RSDA"

data(abalone.iGAP)
int_detect_format(abalone.iGAP)  # Should return "iGAP"

# ARRAY format
x <- array(1:24, dim = c(4, 3, 2))
int_detect_format(x)  # Should return "ARRAY"

List Available Format Conversions

Description

List all available format conversion functions.

Usage

int_list_conversions(from = NULL, to = NULL)

Arguments

Value

A data.frame showing available conversions

Examples

# List all conversions
int_list_conversions()

# List conversions from RSDA
int_list_conversions(from = "RSDA")

# List conversions to MM
int_list_conversions(to = "MM")

Distance Measures for Interval Data

Description

Functions to compute various distance measures between interval-valued observations.

int_dist_all computes all available distance measures at once.

Usage

int_dist(x, method = "euclidean", gamma = 0.5, q = 1, p = 2, ...)

int_dist_matrix(x, method = "euclidean", gamma = 0.5, q = 1, p = 2, ...)

int_pairwise_dist(x, var_name1, var_name2, method = "euclidean", ...)

int_dist_all(x, gamma = 0.5, q = 1)

Arguments

Details

Available distance methods:

• GD: Gowda-Diday distance (Gowda & Diday, 1991)

• IY: Ichino-Yaguchi distance (Ichino, 1988)

• L1: L1 (midpoint Manhattan) distance

• L2: L2 (Euclidean midpoint) distance

• CB: City-Block distance (Souza & de Carvalho, 2004)

• HD: Hausdorff distance (Chavent & Lechevallier, 2002)

• EHD: Euclidean Hausdorff distance

• nEHD: Normalized Euclidean Hausdorff distance

• snEHD: Span Normalized Euclidean Hausdorff distance

• TD: Tran-Duckstein distance (Tran & Duckstein, 2002)

• WD: L2-Wasserstein distance (Verde & Irpino, 2008)

• euclidean: Euclidean distance on interval centers (same as L2)

• hausdorff: Hausdorff distance (same as HD)

• manhattan: Manhattan distance (same as L1)

• city_block: City-block distance (same as CB)

• minkowski: Minkowski distance with parameter p

• wasserstein: Wasserstein distance (same as WD)

• ichino: Ichino-Yaguchi distance (simplified version)

• de_carvalho: De Carvalho distance

Value

A distance matrix (class 'dist') or numeric vector

Author(s)

Han-Ming Wu

References

Gowda, K. C., & Diday, E. (1991). Symbolic clustering using a new dissimilarity measure. Pattern Recognition, 24(6), 567-578.

Ichino, M. (1988). General metrics for mixed features. Systems and Computers in Japan, 19(2), 37-50.

Chavent, M., & Lechevallier, Y. (2002). Dynamical clustering of interval data. In Classification, Clustering and Data Analysis (pp. 53-60). Springer.

Tran, L., & Duckstein, L. (2002). Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets and Systems, 130, 331-341.

Verde, R., & Irpino, A. (2008). A new interval data distance based on the Wasserstein metric.

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

See Also

int_dist_matrix int_dist_all int_pairwise_dist

Examples

# Using symbolic_tbl format
data(mushroom.int)
d1 <- int_dist(mushroom.int[, 3:4], method = "euclidean")
d2 <- int_dist(mushroom.int[, 3:4], method = "hausdorff")
d3 <- int_dist(mushroom.int[, 3:4], method = "GD")

# Using array format: 4 concepts, 3 variables
x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow=4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow=4)
d4 <- int_dist(x, method = "snEHD")
d5 <- int_dist(x, method = "IY", gamma = 0.3)

Geometric Properties of Interval Data

Description

Functions to compute geometric characteristics of interval-valued data.

Usage

int_width(x, var_name, ...)

int_radius(x, var_name, ...)

int_center(x, var_name, ...)

int_overlap(x, var_name1, var_name2, ...)

int_containment(x, var_name1, var_name2, ...)

int_midrange(x, var_name, ...)

Arguments

Details

These functions compute basic geometric properties:

• int_width: Width of each interval (upper - lower)

• int_radius: Radius of each interval (width / 2)

• int_center: Center point of each interval ((lower + upper) / 2)

• int_overlap: Overlap measure between two interval variables

• int_containment: Check if one interval contains another

• int_midrange: Half-range of each interval ((upper - lower) / 2)

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_width int_radius int_center int_overlap

Examples

data(mushroom.int)

# Calculate interval widths
int_width(mushroom.int, var_name = "Pileus.Cap.Width")
int_width(mushroom.int, var_name = 2:3)

# Calculate interval radius
int_radius(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Get interval centers
int_center(mushroom.int, var_name = 2:4)

# Measure overlap between two variables
int_overlap(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Check containment
int_containment(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Calculate midrange
int_midrange(mushroom.int, var_name = 2:3)

Position and Scale Measures for Interval Data

Description

Functions to compute position and scale statistics for interval-valued data.

Usage

int_median(x, var_name, method = "CM", ...)

int_quantile(x, var_name, probs = c(0.25, 0.5, 0.75), method = "CM", ...)

int_range(x, var_name, method = "CM", ...)

int_iqr(x, var_name, method = "CM", ...)

int_mad(x, var_name, method = "CM", ...)

int_mode(x, var_name, method = "CM", breaks = 30, ...)

Arguments

Details

These functions provide position and scale measures:

• int_median: Median of interval data

• int_quantile: Quantiles of interval data

• int_range: Range (max - min) of interval data

• int_iqr: Interquartile range (Q3 - Q1)

• int_mad: Median absolute deviation

• int_mode: Mode of interval data (estimated via histogram)

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_median int_quantile

Examples

data(mushroom.int)

# Calculate median
int_median(mushroom.int, var_name = "Pileus.Cap.Width")
int_median(mushroom.int, var_name = 2:3, method = c("CM", "EJD"))

# Calculate quantiles
int_quantile(mushroom.int, var_name = 2, probs = c(0.25, 0.5, 0.75))

# Calculate interquartile range
int_iqr(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Calculate range
int_range(mushroom.int, var_name = "Pileus.Cap.Width")

# Calculate MAD
int_mad(mushroom.int, var_name = 2:3, method = "CM")

# Estimate mode
int_mode(mushroom.int, var_name = "Stipe.Length", method = "CM")

Robust Statistics for Interval Data

Description

Functions to compute robust statistics for interval-valued data.

Usage

int_trimmed_mean(x, var_name, trim = 0.1, method = "CM", ...)

int_winsorized_mean(x, var_name, trim = 0.1, method = "CM", ...)

int_trimmed_var(x, var_name, trim = 0.1, method = "CM", ...)

int_winsorized_var(x, var_name, trim = 0.1, method = "CM", ...)

Arguments

Details

These functions provide robust alternatives to standard statistics:

• int_trimmed_mean: Mean after trimming extreme values

• int_winsorized_mean: Mean after winsorizing extreme values

• int_trimmed_var: Variance after trimming extreme values

• int_winsorized_var: Variance after winsorizing extreme values

Trimming vs Winsorizing:

• Trimming: Remove extreme values

• Winsorizing: Replace extreme values with less extreme values

Value

A numeric matrix

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_trimmed_mean

Examples

data(mushroom.int)

# Trimmed mean (10% from each end)
int_trimmed_mean(mushroom.int, var_name = "Pileus.Cap.Width", trim = 0.1)

# Winsorized mean
int_winsorized_mean(mushroom.int, var_name = 2:3, trim = 0.05, method = "CM")

# Trimmed variance
int_trimmed_var(mushroom.int, var_name = c("Stipe.Length"), trim = 0.1)

Distribution Shape Measures for Interval Data

Description

Functions to compute shape statistics (skewness, kurtosis) for interval-valued data.

Usage

int_skewness(x, var_name, method = "CM", ...)

int_kurtosis(x, var_name, method = "CM", ...)

int_symmetry(x, var_name, method = "CM", ...)

int_tailedness(x, var_name, method = "CM", ...)

Arguments

Details

These functions measure distribution shape:

• int_skewness: Measure of asymmetry (skewness)

• int_kurtosis: Measure of tail heaviness (kurtosis)

• int_symmetry: Symmetry coefficient

• int_tailedness: Tailedness measure (alias for excess kurtosis)

Skewness interpretation:

• = 0: Symmetric distribution

• > 0: Right-skewed (positive skew)

• < 0: Left-skewed (negative skew)

Kurtosis interpretation (excess kurtosis):

• = 0: Normal distribution (mesokurtic)

• > 0: Heavy tails (leptokurtic)

• < 0: Light tails (platykurtic)

Value

A numeric matrix

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_skewness int_kurtosis

Examples

data(mushroom.int)

# Calculate skewness
int_skewness(mushroom.int, var_name = "Pileus.Cap.Width")
int_skewness(mushroom.int, var_name = 2:3, method = c("CM", "EJD"))

# Calculate kurtosis
int_kurtosis(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Check symmetry
int_symmetry(mushroom.int, var_name = 2:4, method = "CM")

# Check tailedness
int_tailedness(mushroom.int, var_name = "Pileus.Cap.Width", method = "CM")

Similarity Measures for Interval Data

Description

Functions to compute similarity measures between interval-valued observations.

Usage

int_jaccard(x, var_name1, var_name2, ...)

int_dice(x, var_name1, var_name2, ...)

int_cosine(x, var_name1, var_name2, ...)

int_overlap_coefficient(x, var_name1, var_name2, ...)

int_tanimoto(x, var_name1, var_name2, ...)

int_similarity_matrix(x, method = "jaccard", ...)

Arguments

Details

These functions compute various similarity measures:

• int_jaccard: Jaccard similarity coefficient

• int_dice: Dice similarity coefficient

• int_cosine: Cosine similarity

• int_overlap_coefficient: Overlap coefficient

• int_tanimoto: Tanimoto coefficient (generalized Jaccard)

• int_similarity_matrix: Pairwise similarity matrix across all observations

All similarity measures range from 0 (no similarity) to 1 (perfect similarity).

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_dist int_cor int_jaccard

Examples

data(mushroom.int)

# Jaccard similarity
int_jaccard(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Dice coefficient
int_dice(mushroom.int, 2, 3)

# Cosine similarity
int_cosine(mushroom.int, 
           var_name1 = c("Pileus.Cap.Width"), 
           var_name2 = c("Stipe.Length", "Stipe.Thickness"))

# Overlap coefficient
int_overlap_coefficient(mushroom.int, 2, 3:4)

# Tanimoto coefficient
int_tanimoto(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Similarity matrix across all observations
int_similarity_matrix(mushroom.int, method = "jaccard")

Statistics for Interval Data

Description

Functions to compute the mean, variance, covariance, and correlation of interval-valued data.

Usage

int_mean(x, var_name, method = "CM", ...)

int_var(x, var_name, method = "CM", ...)

int_cov(x, var_name1, var_name2, method = "CM", ...)

int_cor(x, var_name1, var_name2, method = "CM", ...)

Arguments

Details

Available methods (applicable to all four functions):

• CM: Center Method — uses midpoints (a + b) / 2

• VM: Vertices Method — uses all 2^p vertex combinations

• QM: Quantiles Method — uses equally spaced quantile points

• SE: Set Expansion — uses endpoints only (quantiles with m = 1)

• FV: Fitted Values — uses linear regression fitted values

• EJD: Empirical Joint Distribution

• GQ: Symbolic Covariance method (Billard and Diday, 2006)

• SPT: Total Sum of Products (Billard, 2008)

Value

A numeric matrix for int_mean and int_var (methods x variables); a named list of covariance/correlation matrices for int_cov and int_cor (one matrix per method).

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_cov int_cor

Examples

data(mushroom.int)
int_mean(mushroom.int, var_name = "Pileus.Cap.Width")
int_mean(mushroom.int, var_name = 2:3)

var_name <- c("Stipe.Length", "Stipe.Thickness")
method <- c("CM", "FV", "EJD")
int_mean(mushroom.int, var_name, method)
int_var(mushroom.int, var_name, method)

var_name1 <- "Pileus.Cap.Width"
var_name2 <- c("Stipe.Length", "Stipe.Thickness")
method <- c("CM", "VM", "EJD", "GQ", "SPT")
int_cov(mushroom.int, var_name1, var_name2, method)
int_cor(mushroom.int, var_name1, var_name2, method)

Uncertainty and Variability Measures for Interval Data

Description

Functions to compute uncertainty and variability measures for interval-valued data.

Usage

int_entropy(x, var_name, method = "CM", base = 2, ...)

int_cv(x, var_name, method = "CM", ...)

int_dispersion(x, var_name, method = "CM", ...)

int_imprecision(x, var_name, ...)

int_granularity(x, var_name, ...)

int_uniformity(x, var_name, ...)

int_information_content(x, var_name, method = "CM", ...)

Arguments

Details

These functions measure uncertainty and variability:

• int_entropy: Shannon entropy (information content)

• int_cv: Coefficient of variation (CV = SD / Mean)

• int_dispersion: General dispersion index

• int_imprecision: Imprecision based on interval width

• int_granularity: Variability in interval sizes

• int_uniformity: Uniformity of interval widths (inverse of granularity)

• int_information_content: Normalized entropy (entropy / log2(n))

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_var int_entropy int_cv

Examples

data(mushroom.int)

# Calculate entropy
int_entropy(mushroom.int, var_name = "Pileus.Cap.Width")

# Coefficient of variation
int_cv(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"), method = c("CM", "EJD"))

# Measure imprecision
int_imprecision(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Dispersion index
int_dispersion(mushroom.int, var_name = "Pileus.Cap.Width", method = "CM")

# Check data granularity
int_granularity(mushroom.int, var_name = 2:4)

# Check uniformity
int_uniformity(mushroom.int, var_name = 2:3)

# Information content
int_information_content(mushroom.int, var_name = "Stipe.Length", method = "CM")

Internal Utility Functions for Interval Data

Description

Internal functions for interval data transformation. These are used by the exported interval statistics functions (int_mean, int_var, int_cov, int_cor) and are not intended to be called directly.

Details

Internal Utility Functions for Interval Data

Iris Species Interval Dataset

Description

Interval-valued version of the classic iris dataset, aggregated from Fisher's iris data into 30 interval observations across 3 species (Setosa, Versicolor, Virginica). Each observation represents a group of flowers with ranges for sepal and petal measurements.

Usage

data(iris.int)

Format

A data frame with 30 observations and 5 variables:

• sepal_length: Sepal length range (cm).

• sepal_width: Sepal width range (cm).

• petal_length: Petal length range (cm).

• petal_width: Petal width range (cm).

• class: Species (Setosa, Versicolor, Virginica).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(iris.int)

Iris Species Histogram-Valued Dataset

Description

Histogram-valued dataset of 3 iris species (Versicolor, Virginica, Setosa) with 4 histogram-valued morphological variables and a species label. Each histogram describes the distribution of measurements within a species.

Usage

data(iris_species.hist)

Format

A data frame with 3 observations and 5 variables:

• species: Species name (factor: Versicolor, Virginica, Setosa).

• sepal_width: Histogram-valued sepal width distribution.

• sepal_length: Histogram-valued sepal length distribution.

• petal_width: Histogram-valued petal width distribution.

• petal_length: Histogram-valued petal length distribution.

Row names are species names.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 4-10.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 4-10.

Examples

data(iris_species.hist)

Irish Wind Speed Monthly Interval Time Series

Description

Monthly interval-valued wind speed data at 5 meteorological stations in Ireland from January 1961 to December 1978 (216 months). For each month and station, the interval is defined as [minimum daily average wind speed, maximum daily average wind speed] across all days in that month.

Usage

data(irish_wind.its)

Format

A data frame with 216 observations and 11 columns (5 interval variables in _l/_u Min-Max pairs, plus a date):

• date: First day of the month (Date class).

• BIR_l, BIR_u: Monthly [min, max] daily wind speed at Birr (knots).

• DUB_l, DUB_u: Monthly [min, max] daily wind speed at Dublin Airport (knots).

• KIL_l, KIL_u: Monthly [min, max] daily wind speed at Kilkenny (knots).

• SHA_l, SHA_u: Monthly [min, max] daily wind speed at Shannon Airport (knots).

• VAL_l, VAL_u: Monthly [min, max] daily wind speed at Valentia Observatory (knots).

Details

The original data contains daily average wind speeds (in knots) at 12 synoptic meteorological stations in the Republic of Ireland, collected by the Irish Meteorological Service. This is the classic Haslett and Raftery (1989) dataset, one of the most widely used benchmarks in spatial statistics. Following the approach of Teles and Brito (2015), the raw daily data is aggregated to monthly intervals for 5 selected stations: Birr (BIR), Dublin Airport (DUB), Kilkenny (KIL), Shannon Airport (SHA), and Valentia Observatory (VAL). Each monthly interval captures the range of daily wind variability within that month.

Metadata

Source

Derived from the wind dataset in the gstat R package (originally from Haslett and Raftery, 1989). Daily data aggregated to monthly intervals.

References

Haslett, J. and Raftery, A. E. (1989). Space-time modelling with long-memory dependence: Assessing Ireland's wind power resource. Journal of the Royal Statistical Society, Series C (Applied Statistics), 38(1), 1–50.

Teles, P. and Brito, P. (2015). Modeling interval time series with space-time processes. Communications in Statistics – Theory and Methods, 44(17), 3599–3619.

Examples

data(irish_wind.its)
head(irish_wind.its)
# Plot Valentia Observatory wind speed interval
plot(irish_wind.its$date, irish_wind.its$VAL_u, type = "l", col = "red",
     ylab = "Wind speed (knots)", xlab = "Date",
     main = "Valentia Observatory Monthly Wind Speed Interval")
lines(irish_wind.its$date, irish_wind.its$VAL_l, col = "blue")
legend("topright", c("Max", "Min"), col = c("red", "blue"), lty = 1)

Joggers Mixed Symbolic Dataset

Description

Mixed symbolic dataset of 10 jogger groups with one interval-valued variable (pulse rate) and one histogram-valued variable (running time distribution).

Usage

data(joggers.mix)

Format

A symbolic data frame (symbolic_tbl) with 10 observations (jogger groups) and 2 variables:

• pulse_rate: Interval-valued resting pulse rate range (bpm).

• running_time: Histogram-valued distribution of running times (minutes).

Row names are Group_1 through Group_10.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 2-5.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 2-5.

Examples

data(joggers.mix)

Judge 1 Interval-Valued Ratings

Description

Interval-valued ratings from Judge 1 for 6 regions on 4 variables. From a study of generalized principal component analysis for interval-valued data (GPCSIV).

Usage

data(judge1.int)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 4 interval-valued variables (V1–V4).

Metadata

Source

GPCSIV R package (Judge1 dataset).

References

Makosso-Kallyth, S. and Diday, E. (2012). Adaptation of interval PCA to symbolic histogram variables. Advances in Data Analysis and Classification, 6(2), 147–159.

Original data from the GPCSIV R package (Judge1 dataset).

Examples

data(judge1.int)

Judge 2 Interval-Valued Ratings

Description

Interval-valued ratings from Judge 2 for 6 regions on 4 variables. From a study of generalized principal component analysis for interval-valued data (GPCSIV).

Usage

data(judge2.int)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 4 interval-valued variables (V1–V4).

Metadata

Source

GPCSIV R package (Judge2 dataset).

References

Makosso-Kallyth, S. and Diday, E. (2012). Adaptation of interval PCA to symbolic histogram variables. Advances in Data Analysis and Classification, 6(2), 147–159.

Original data from the GPCSIV R package (Judge2 dataset).

Examples

data(judge2.int)

Judge 3 Interval-Valued Ratings

Description

Interval-valued ratings from Judge 3 for 6 regions on 4 variables. From a study of generalized principal component analysis for interval-valued data (GPCSIV).

Usage

data(judge3.int)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 4 interval-valued variables (V1–V4).

Metadata

Source

GPCSIV R package (Judge3 dataset).

References

Makosso-Kallyth, S. and Diday, E. (2012). Adaptation of interval PCA to symbolic histogram variables. Advances in Data Analysis and Classification, 6(2), 147–159.

Original data from the GPCSIV R package (Judge3 dataset).

Examples

data(judge3.int)

Lack of Information Questionnaire Interval Dataset

Description

Interval-valued dataset from a lack-of-information questionnaire. Contains biographical data and responses to 5 items measuring perception of lack of information, collected via an interval-valued Likert scale.

Usage

data(lackinfo.int)

Format

A data frame with 50 observations and 8 variables:

• id: Identification number.

• sex: Sex of the respondent (male or female).

• age: Respondent's age (in years).

• item1: Interval-valued answer to item 1.

• item2: Interval-valued answer to item 2.

• item3: Interval-valued answer to item 3.

• item4: Interval-valued answer to item 4.

• item5: Interval-valued answer to item 5.

Details

An educational innovation project was carried out for improving teaching-learning processes at the University of Oviedo (Spain) for the 2020/2021 academic year. A total of 50 students answered an online questionnaire about biographical data (sex and age) and their perception of lack of information by selecting the interval that best represents their level of agreement on a scale bounded between 1 (strongly disagree) and 7 (strongly agree).

The 5 items measuring perception of lack of information are:

• I1: I receive too little information from my classmates.

• I2: It is difficult to receive relevant information from my classmates.

• I3: It is difficult to receive relevant information from the teacher.

• I4: The amount of information I receive from my classmates is very low.

• I5: The amount of information I receive from the teacher is very low.

Metadata

Source

https://CRAN.R-project.org/package=IntervalQuestionStat

Examples

data(lackinfo.int)

Lisbon Air Quality Daily Interval Dataset

Description

Interval-valued daily air quality data from the Entrecampos monitoring station in Lisbon, Portugal, covering 2019–2021 (1096 days). Each day's pollutant concentration is represented as a [\min, \max] interval from hourly measurements. Missing days are imputed via linear interpolation.

Usage

data(lisbon_air_quality.int)

Format

A symbolic data frame (symbolic_tbl) with 1096 observations (daily) and 8 interval-valued pollutant variables:

• so2: Sulphur dioxide (ug/m3).

• pm10: Particulate matter < 10 um (ug/m3).

• o3: Ozone (ug/m3).

• no2: Nitrogen dioxide (ug/m3).

• co: Carbon monoxide (ug/m3).

• pm25: Particulate matter < 2.5 um (ug/m3).

• nox: Nitrogen oxides (ug/m3).

• no: Nitric oxide (ug/m3).

Metadata

Source

QualAr, Entrecampos station, Lisbon, Portugal.

References

Dias, S. and Brito, P. (2017). Off the beaten track: A new linear model for interval data. European Journal of Operational Research, 258(3), 1118–1130.

Data from the QualAr Portuguese air quality monitoring network (‘⁠https://qualar.apambiente.pt/⁠’).

Examples

data(lisbon_air_quality.int)

Loans by Purpose Interval Dataset

Description

Interval-valued data for loan characteristics aggregated by their purpose. Original microdata contains 887,383 loan records from Kaggle.

Usage

data(loans_by_purpose.int)

Format

A data frame with 14 observations and 4 interval-valued variables:

• ln_inc: Natural logarithm of self-reported annual income.

• ln_revolbal: Natural logarithm of total credit revolving balance.

• open_acc: Number of open credit lines.

• total_acc: Total number of credit lines.

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

Examples

data(loans_by_purpose.int)

Lending Club Loans by Risk Level

Description

Interval-valued dataset of 35 Lending Club loan groups classified by risk level (A through G, 5 groups each). Each group is described by 4 interval-valued financial variables.

Usage

data(loans_by_risk.int)

Format

A symbolic data frame (symbolic_tbl) with 35 observations and 5 variables:

• log_income: Interval-valued log annual income.

• interest_rate: Interval-valued interest rate (%).

• open_accounts: Interval-valued number of open credit accounts.

• total_accounts: Interval-valued total number of credit accounts.

• risk_level: Risk grade factor (A, B, C, D, E, F, G).

Row names are A1–A5, B1–B5, ..., G1–G5.

Metadata

Source

MAINT.Data R package (LoansbyRisk_minmax dataset).

References

Brito, P. and Duarte Silva, A.P. (2012). Modelling interval data with Normal and Skew-Normal distributions. Journal of Applied Statistics, 39(1), 3–20.

Original data from the MAINT.Data R package.

Examples

data(loans_by_risk.int)

Lending Club Loans by Risk Level (Quantile-Based Intervals)

Description

Interval-valued dataset of 35 Lending Club loan groups stratified by risk level (A1–G5). Intervals represent the 10th to 90th percentile range of each financial variable within each risk subgrade.

Usage

data(loans_by_risk_quantile.int)

Format

A symbolic data frame (symbolic_tbl) with 35 observations and 4 variables:

• ln-inc: Interval-valued log income.

• int-rate: Interval-valued interest rate.

• open-acc: Interval-valued number of open accounts.

• total-acc: Interval-valued total accounts.

Metadata

Source

MAINT.Data R package (LoansbyRiskLvs_qntlDt dataset).

References

Brito, P. and Duarte Silva, A.P. (2012). Modelling interval data with Normal and Skew-Normal distributions. Journal of Applied Statistics, 39(1), 3–20.

Original data from the MAINT.Data R package (LoansbyRiskLvs_qntlDt dataset).

Examples

data(loans_by_risk_quantile.int)

Lung Cancer Treatments by State Histogram-Valued Dataset

Description

Histogram-valued distribution of lung cancer treatment counts for 2 US states (Massachusetts and New York).

Usage

data(lung_cancer.hist)

Format

A data frame with 2 observations and 2 variables:

• state: State name (character).

• y30: Histogram-valued distribution of treatment counts as a weighted set string (e.g., "{0, 0.77; 1, 0.08; 2, 0.15}").

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.20.

Examples

data(lung_cancer.hist)

Lynne1 Blood Pressure Interval Dataset

Description

Interval-valued dataset of 10 observations with pulse rate, systolic pressure, and diastolic pressure intervals.

Usage

data(lynne1.int)

Format

A symbolic data frame (symbolic_tbl) with 10 observations and 4 variables:

• concept: Character concept label.

• Pulse Rate: Interval-valued pulse rate (beats/min).

• Systolic Pressure: Interval-valued systolic pressure (mmHg).

• Diastolic Pressure: Interval-valued diastolic pressure (mmHg).

Metadata

Source

RSDA R package (Lynne1 dataset).

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester.

Original data from the RSDA R package (Lynne1 dataset).

Examples

data(lynne1.int)

MERVAL Index Weekly Min/Max Interval Time Series

Description

Weekly minimum and maximum values of the Argentine MERVAL stock market index from January 4, 2016 to September 28, 2020 (248 weeks). Daily data was downloaded and aggregated to weekly intervals. This dataset matches the period used by de Carvalho and Martos (2022).

Usage

data(merval.its)

Format

A data frame with 248 observations and 3 variables:

• date: Week start date, Monday (Date class).

• low: Weekly minimum of daily low values.

• high: Weekly maximum of daily high values.

Details

The MERVAL (Mercado de Valores de Buenos Aires) is the main stock market index of the Buenos Aires Stock Exchange. Each observation represents one week, with the weekly low computed as the minimum of daily lows and the weekly high computed as the maximum of daily highs. The date column indicates the Monday (start) of each week. This period covers the Argentine economic crisis and the early COVID-19 pandemic impact.

Metadata

Source

Yahoo Finance, ticker ^MERV. Downloaded via the quantmod package and aggregated from daily to weekly.

References

de Carvalho, F. A. T. and Martos, G. (2022). Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series. Journal of Forecasting, 41(1), 167–180.

Examples

data(merval.its)
head(merval.its)
plot(merval.its$date, merval.its$high, type = "l", col = "red",
     ylab = "Index Value", xlab = "Date",
     main = "MERVAL Weekly Min/Max (2016-2020)")
lines(merval.its$date, merval.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Motor Trend Cars Mixed Symbolic Dataset

Description

Mixed symbolic dataset of 5 car groups from the mtcars data, with 7 interval-valued performance variables and 4 modal-valued categorical variables.

Usage

data(mtcars.mix)

Format

A symbolic data frame (symbolic_tbl) with 5 observations (car groups) and 11 variables:

• mpg: Interval-valued miles per gallon.

• cyl: Modal-valued number of cylinders.

• disp: Interval-valued displacement (cu.in.).

• hp: Interval-valued horsepower.

• drat: Interval-valued rear axle ratio.

• wt: Interval-valued weight (1000 lbs).

• qsec: Interval-valued quarter-mile time (seconds).

• vs: Modal-valued engine type (V/S).

• am: Modal-valued transmission type (auto/manual).

• gear: Modal-valued number of forward gears.

• carb: Modal-valued number of carburetors.

Metadata

Source

ggESDA R package (mtcars.i dataset).

References

Henderson, R. and Velleman, P. (1981). Building multiple regression models interactively. Biometrics, 37, 391–411.

Original data from the ggESDA R package (mtcars.i dataset).

Examples

data(mtcars.mix)

Mushroom Species Interval Dataset

Description

Interval-valued version of the mushroom dataset. See mushroom.int.mm.

Usage

data(mushroom.int)

Format

A symbolic data frame (symbolic_tbl) with 23 observations and 5 variables:

• Species: Mushroom species name (character).

• Pileus.Cap.Width: Pileus cap width range (cm, interval).

• Stipe.Length: Stipe length range (cm, interval).

• Stipe.Thickness: Stipe thickness range (cm, interval).

• Edibility: Edibility code (U = Unknown, Y = Yes, N = No, T = Toxic; character).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 3.2.

Examples

data(mushroom.int)

Mushroom Species Dataset (Original Format)

Description

Interval-valued data for 23 mushroom species of the genus Agaricus with 3 morphological measurements from the Fungi of California Species.

Usage

data(mushroom.int.mm)

Format

A data frame with 23 observations and 5 variables:

• Species: Mushroom species name.

• Pileus.Cap.Width: Pileus cap width range (cm).

• Stipe.Length: Stipe length range (cm).

• Stipe.Thickness: Stipe thickness range (cm).

• Edibility: Edibility code (U/Y/N/T).

Details

Classic SDA dataset used for descriptive statistics, histogram construction, and clustering of interval-valued data.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 3.2.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 3.2.

Examples

data(mushroom.int.mm)

Mushroom Species Fuzzy/Symbolic Dataset

Description

Extended mushroom data with fuzzy stipe thickness (Small/Average/Large), numerical stipe length, interval cap size, and categorical cap colour for two Amanita species (4 specimens).

Usage

data(mushroom_fuzzy.mix)

Format

A data frame with 4 observations (Mushroom1–Mushroom4) and 9 variables:

• specimen: Specimen identifier (character).

• species: Species name (character).

• stipe_thickness: Stipe thickness measurement (numeric, cm).

• fuzzy_small: Fuzzy membership degree for Small (numeric, 0–1).

• fuzzy_average: Fuzzy membership degree for Average (numeric, 0–1).

• fuzzy_large: Fuzzy membership degree for Large (numeric, 0–1).

• stipe_length: Stipe length (numeric, cm).

• cap_size: Cap size as interval string (e.g., "24 +/- 1", character).

• cap_colour: Cap colour (character).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Tables 1.14-1.16.

Examples

data(mushroom_fuzzy.mix)

New York City Flights Interval Dataset

Description

Interval-valued dataset with 142 units and four interval-valued variables from the nycflights13 package, aggregated by month and carrier.

Usage

data(nycflights.int)

Format

A symbolic data frame (symbolic_tbl) with 142 observations and 5 variables:

• X: Month-carrier identifier (character).

• dep_delay: Departure delay range (minutes, interval).

• arr_delay: Arrival delay range (minutes, interval).

• air_time: Air time range (minutes, interval).

• distance: Distance range (miles, interval).

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

References

Duarte Silva, A.P., Brito, P., Filzmoser, P. and Dias, J.G. (2021). MAINT.Data: Modelling and Analysing Interval Data in R. R Journal, 13(2).

Examples

data(nycflights.int)

Occupation Salaries Dataset

Description

Modal-valued dataset of 9 occupations with gender and salary distributions. This is the wide (flat table) format; see occupations2.modal for the modal-valued version.

Usage

data(occupations.modal)

Format

A data frame with 9 observations and 11 columns:

• Occupation: Occupation name (character).

• Gender(M), Gender(F): Proportion male/female (2 bins).

• Salary(1) through Salary(7): Salary distribution across 7 ordered bins (proportions).

• n: Sample size (integer).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(occupations.modal)

Occupation Salaries Modal-Valued Dataset

Description

Modal-valued version of the occupation salaries dataset. See occupations.modal for the wide-format version.

Usage

data(occupations2.modal)

Format

A symbolic data frame (symbolic_tbl) with 9 observations and 4 variables:

• Occupation: Occupation name (character).

• Gender: Modal distribution over gender (Male, Female).

• Salary: Modal distribution over 7 ordered salary bins.

• n: Sample size (numeric).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(occupations2.modal)

Ohio River Basin 30-Year Trimmed Mean Daily Temperatures Interval Dataset

Description

Interval-valued dataset of 30-year trimmed mean daily temperatures for the Ohio river basin. Intervals are defined by the mean daily maximum and minimum temperatures from January 1, 1988 to December 31, 2018.

Usage

data(ohtemp.int)

Format

A data frame with 161 rows and 7 variables:

• ID: Global Historical Climatological Network (GHCN) station identifier.

• NAME: GHCN station name.

• STATE: Two-digit state designation.

• LATITUDE: Latitude coordinate position.

• LONGITUDE: Longitude coordinate position.

• ELEVATION: Elevation of the measurement location (meters).

• TEMPERATURE: 30-year mean daily temperature (tenths of degrees Celsius).

Metadata

Source

https://CRAN.R-project.org/package=intkrige

Examples

data(ohtemp.int)

Oils and Fats Interval Dataset

Description

Classic benchmark interval-valued data for 8 oils and fats described by 4 physico-chemical properties. Originally from Ichino (1988).

Usage

data(oils.int)

Format

A data frame with 8 observations and 9 columns (4 interval variables in _l/_u Min-Max pairs, plus a label):

• sample: Oil/fat sample name (character).

• specific_gravity_l, specific_gravity_u: Specific gravity range.

• freezing_point_l, freezing_point_u: Freezing point range (degrees Celsius).

• iodine_value_l, iodine_value_u: Iodine value range.

• saponification_value_l, saponification_value_u: Saponification value range.

Details

The 8 samples are: Linseed oil, Perilla oil, Cottonseed oil, Sesame oil, Camellia oil, Olive oil, Beef tallow, Hog fat. The expected 3-cluster structure is: {Beef tallow, Hog fat}, {Cottonseed, Sesame, Camellia, Olive}, and {Linseed, Perilla}. Widely used for comparing clustering methods and distance measures in symbolic data analysis.

Metadata

References

Ichino, M. (1988). General metrics for mixed features. Proc. IEEE Conf. Systems, Man, and Cybernetics, pp. 494-497.

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 13.7, p.253.

Examples

data(oils.int)

Ozone Air Quality Histogram-Valued Dataset

Description

Histogram-valued dataset of 84 daily observations with 4 weather-related histogram variables. Each histogram has 10 equal-probability (decile) bins summarizing hourly measurements within each day.

Usage

data(ozone.hist)

Format

A data frame with 84 observations (days) and 4 histogram-valued variables:

• Ozone.Conc.ppb: Histogram of ozone concentration (ppb).

• Temperature.C: Histogram of temperature (Celsius).

• Solar.Radiation.WattM2: Histogram of solar radiation (W/m^2).

• Wind.Speed.mSec: Histogram of wind speed (m/s).

Row names are I1 through I84.

Metadata

Source

HistDAWass R package (OzoneH dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: A new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (OzoneH dataset), reduced from 100 quantile bins to 10 decile bins.

Examples

data(ozone.hist)

Petrobras Stock Daily High/Low Interval Time Series

Description

Daily high and low stock prices of Petrobras (ADR traded on NYSE) from January 3, 2005 to December 29, 2006 (503 trading days). This dataset matches the period used by Maia, de Carvalho and Ludermir (2008) in their work on forecasting models for interval-valued time series.

Usage

data(petrobras.its)

Format

A data frame with 503 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price (USD).

• high: Daily high price (USD).

Details

Petrobras (Petroleo Brasileiro S.A.) is the Brazilian multinational petroleum corporation. The ADR (American Depositary Receipt) is traded on the New York Stock Exchange under ticker PBR. Each observation represents a trading day with the daily low and high prices forming an interval. This was one of the first datasets used to demonstrate interval-valued autoregressive (iAR) models.

Metadata

Source

Yahoo Finance, ticker PBR. Downloaded via the quantmod package.

References

Maia, A. L. S., de Carvalho, F. A. T. and Ludermir, T. B. (2008). Forecasting models for interval-valued time series. Neurocomputing, 71(16–18), 3344–3352.

Examples

data(petrobras.its)
head(petrobras.its)
plot(petrobras.its$date, petrobras.its$high, type = "l", col = "red",
     ylab = "Price (USD)", xlab = "Date",
     main = "Petrobras Daily High/Low (2005-2006)")
lines(petrobras.its$date, petrobras.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Polish Car Models Mixed Symbolic Dataset

Description

Mixed symbolic dataset of 30 car models sold in Poland, with 9 interval-valued technical specification variables and 3 multinomial-valued categorical variables.

Usage

data(polish_cars.mix)

Format

A symbolic data frame (symbolic_tbl) with 30 observations and 12 variables:

• price: Interval-valued price (PLN).

• body: Multinomial body types (e.g., hatchback, sedan, combi).

• wheelbase: Interval-valued wheelbase (mm).

• chassis_length: Interval-valued chassis length (mm).

• chassis_width: Interval-valued chassis width (mm).

• chassis_height: Interval-valued chassis height (mm).

• engine_capacity: Multinomial engine displacement categories (litres).

• engine_power: Interval-valued engine power (HP).

• maximum_speed: Interval-valued maximum speed (km/h).

• acceleration: Interval-valued 0–100 km/h time (seconds).

• fuel_type: Multinomial fuel types (petrol, diesel, LPG).

• fuel_consumption: Interval-valued fuel consumption (L/100km).

Metadata

Source

symbolicDA R package (cars dataset).

References

Dudek, A. and Pelka, M. (2012). symbolicDA: Analysis of Symbolic Data. R package.

Examples

data(polish_cars.mix)

Polish Voivodships Socio-Economic Intervals

Description

Interval-valued dataset of 18 Polish voivodships (administrative regions) with 9 socio-economic interval variables describing demographic and economic characteristics at the county (powiat) level.

Usage

data(polish_voivodships.int)

Format

A symbolic data frame (symbolic_tbl) with 18 observations (voivodships) and 9 interval-valued variables:

• V1 through V9: Interval-valued socio-economic indicators aggregated across counties within each voivodship.

Row names are voivodship names (e.g., Dolnoslaskie, Lubelskie).

Metadata

Source

clusterSim R package (data_pathtinger dataset).

References

Dudek, A. and Pelka, M. (2022). symbolicDA: Analysis of Symbolic Data. R package.

Walesiak, M. and Dudek, A. (2020). clusterSim: Searching for Optimal Clustering Procedure for a Data Set. R package.

Examples

data(polish_voivodships.int)

Profession Work Salary Time Interval Dataset

Description

Interval-valued data for 15 profession entries classified by work type (White Collar / Blue Collar). Each entry describes a specific profession with salary and working duration ranges.

Usage

data(profession.int)

Format

A symbolic data frame (symbolic_tbl) with 15 observations and 4 variables:

• Type_of_Work: Work category (White Collar or Blue Collar, character).

• Profession: Profession name (character).

• Salary: Salary range (currency units, interval).

• Duration: Working duration range (hours per week, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(profession.int)

Prostate Cancer Clinical Interval Dataset

Description

Interval-valued clinical measurements for 97 prostate cancer patients (training and test sets combined). Contains 9 interval-valued variables from log-transformed cancer volume, weight, age, and other clinical predictors.

Usage

data(prostate.int)

Format

A data frame with 97 observations and 9 interval-valued variables:

• lcavol: Log cancer volume range.

• lweight: Log prostate weight range.

• age: Patient age range.

• lbph: Log benign prostatic hyperplasia amount range.

• svi: Seminal vesicle invasion range.

• lcp: Log capsular penetration range.

• gleason: Gleason score range.

• pgg45: Percentage Gleason scores 4 or 5 range.

• lpsa: Log prostate specific antigen range.

Metadata

Source

Extracted from RSDA package (int_prost_train, int_prost_test).

References

Stamey, T. et al. (1989). Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. II. Radical prostatectomy treated patients. J. Urology, 141(5), 1076-1083.

Examples

data(prostate.int)

Read a Symbolic Data CSV File

Description

Reads an external CSV file containing symbolic data, automatically detects whether the data is interval-valued (min/max pairs or comma-separated), histogram-valued, modal-valued, or another symbolic type, and returns an appropriate R object.

Usage

read_symbolic_csv(
  file,
  sep = ",",
  header = TRUE,
  row.names = NULL,
  stringsAsFactors = FALSE,
  na.strings = c("", "NA"),
  symbolic_type = NULL,
  ...
)

Arguments

Details

The detection heuristic works as follows:

1. Interval (MM): If the file contains paired _min/_max columns the data is returned as-is (MM format).

2. Interval (iGAP): If one or more character columns contain comma-separated numeric pairs (e.g., "1.2,3.4") they are expanded into _min/_max column pairs and the result is returned in MM format.

3. Histogram / Modal: If columns follow a VarName(bin) naming pattern (e.g., Crime(violent)) and the proportions within each variable group sum to approximately 1, the data is classified as histogram or modal. It is returned as a plain data.frame.

4. Other: If none of the above patterns match, the data is returned as a plain data.frame.

Value

A data.frame. Interval data is returned in MM format (paired _min/_max columns). All other symbolic types are returned as plain data frames.

See Also

write_symbolic_csv, int_detect_format, int_convert_format

Examples

# Write then read back an interval dataset
data(mushroom.int.mm)
tmp <- tempfile(fileext = ".csv")
write_symbolic_csv(mushroom.int.mm, tmp)
df <- read_symbolic_csv(tmp)
head(df)

# Write then read back a histogram dataset
data(airline_flights.hist)
tmp2 <- tempfile(fileext = ".csv")
write_symbolic_csv(airline_flights.hist, tmp2)
df2 <- read_symbolic_csv(tmp2)
head(df2)

Search Datasets

Description

Search and filter the dataSDA dataset catalog by metadata criteria including sample size, number of variables, subject area, symbolic format, analytical tasks, keywords, and book reference.

Usage

search_data(...)

Arguments

Details

For character columns (subject, type, task, tag, book), the == operator performs a case-insensitive substring match (using grepl). The type column uses short suffix-based labels that match the dataset name suffix (e.g., type == "int" matches all .int datasets).

For numeric columns (n, p), standard comparison operators are used with exact semantics.

When no arguments are provided, or when tag == "all" is used, all datasets are returned.

Value

A data frame with one row per matching dataset and the following columns: name, n, p, subject, type, task, tag, book.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester.

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley.

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley.

Examples

# List all datasets
search_data()

# Filter by symbolic format (suffix-based)
search_data(type == "hist")

# Filter by analytical task and size
search_data(task == "Regression", n > 10)

# Filter by book reference
search_data(book == "SDA_2006")

# Combine multiple filters
search_data(type == "int", task == "Clustering", subject == "Biology")

# Filter by size range
search_data(n >= 20, n <= 100, p < 10)

Set Variable Format

Description

This function changes the format of the set variables in the data to conform to the RSDA format.

Usage

set_variable_format(data, location = NULL, var = NULL)

Arguments

Value

Return a dataframe in which a set variable is converted to one-hot encoding.

Examples

data("mushroom.int.mm")
mushroom.set <- set_variable_format(data = mushroom.int.mm, location = 8, var = "Species")

Shanghai Stock Exchange Composite Index Daily High/Low Interval Time Series

Description

Daily high and low values of the Shanghai Stock Exchange Composite Index (SSE Composite) from January 2, 2019 to December 30, 2022 (970 trading days). This dataset matches the period used by Yang, Zhang and Wang (2025) for interval time series forecasting.

Usage

data(shanghai_stock.its)

Format

A data frame with 970 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low value of the SSE Composite Index.

• high: Daily high value of the SSE Composite Index.

Details

The SSE Composite Index is the most commonly used indicator to reflect the performance of the Shanghai Stock Exchange. It tracks all stocks (A-shares and B-shares) listed on the exchange. This dataset covers a period that includes the COVID-19 pandemic and its market impacts, providing a rich testbed for evaluating interval forecasting models under extreme volatility.

Metadata

Source

Yahoo Finance, ticker 000001.SS. Downloaded via the quantmod package.

References

Yang, W., Zhang, S. and Wang, S. (2025). On smooth transition interval autoregressive models. Journal of Forecasting, 44(2), 310–332.

Examples

data(shanghai_stock.its)
head(shanghai_stock.its)
plot(shanghai_stock.its$date, shanghai_stock.its$high, type = "l",
     col = "red", ylab = "Index Value", xlab = "Date",
     main = "Shanghai Composite Daily High/Low (2019-2022)")
lines(shanghai_stock.its$date, shanghai_stock.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Simulated Histogram-Valued Dataset

Description

Small simulated histogram-valued dataset of 5 observations with 2 histogram-valued variables. Useful for testing and demonstrating histogram-valued statistical methods.

Usage

data(simulated.hist)

Format

A data frame with 5 observations and 2 histogram-valued variables:

• Y1: Histogram-valued variable 1.

• Y2: Histogram-valued variable 2.

Row names are Obs_1 through Obs_5.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-26.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-26.

Examples

data(simulated.hist)

French Soccer Championship Bivariate Interval Dataset

Description

Interval-valued data for 20 teams from the French premier soccer championship. Contains ranges of Weight (response), Height and Age (explanatory variables).

Usage

data(soccer_bivar.int)

Format

A data frame with 20 rows and 3 interval-valued variables:

• y: Weight (response variable, kg).

• t1: Height (explanatory variable, cm).

• t2: Age (explanatory variable, years).

Metadata

Source

https://CRAN.R-project.org/package=iRegression

References

Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for interval-valued variables. Journal of Statistical Computation and Simulation, 81, 1727-1744.

Examples

data(soccer_bivar.int)

S&P 500 Daily High/Low Interval Time Series

Description

Daily high and low prices of the S&P 500 index from January 2, 2004 to December 30, 2005 (504 trading days). This dataset is a benchmark for interval time series forecasting, matching the period used in the foundational work by Arroyo, Gonzalez-Rivera and Mate (2011).

Usage

data(sp500.its)

Format

A data frame with 504 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price of the S&P 500 index.

• high: Daily high price of the S&P 500 index.

Details

The S&P 500 is a market-capitalization-weighted index of 500 leading publicly traded companies in the United States. Each observation represents a trading day with the daily low and high prices forming an interval. This dataset has been widely used to evaluate interval-valued autoregressive models, exponential smoothing methods for intervals, and center-and-range forecasting approaches.

Metadata

Source

Yahoo Finance, ticker ^GSPC. Downloaded via the quantmod package.

References

Arroyo, J., Gonzalez-Rivera, G. and Mate, C. (2011). Forecasting with interval and histogram data: Some financial applications. In Handbook of Empirical Economics and Finance, pp. 247–280. Chapman and Hall/CRC.

Examples

data(sp500.its)
head(sp500.its)
plot(sp500.its$date, sp500.its$high, type = "l", col = "red",
     ylab = "Price", xlab = "Date", main = "S&P 500 Daily High/Low")
lines(sp500.its$date, sp500.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

State Income Histogram-Valued Dataset

Description

Histogram-valued dataset of 6 US states with 4 income distribution histograms. Each histogram describes the distribution of household income within a state.

Usage

data(state_income.hist)

Format

A data frame with 6 observations (states) and 4 histogram-valued variables:

• Y1 through Y4: Histogram-valued income distribution variables.

Row names are State_1 through State_6.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-18.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-18.

Examples

data(state_income.hist)

Synthetic Interval Clusters Dataset

Description

Synthetic interval-valued dataset with 125 observations in 5 groups of 25 each, described by 6 interval-valued variables and a cluster label. Designed for benchmarking interval data clustering algorithms.

Usage

data(synthetic_clusters.int)

Format

A symbolic data frame (symbolic_tbl) with 125 observations and 7 variables:

• V1 through V6: Six interval-valued variables.

• class: Cluster membership (1–5, set-valued).

Metadata

Source

Extracted from symbolicDA package (data_symbolic).

References

Dudek, A. and Pelka, M. (2022). symbolicDA: Analysis of Symbolic Data. R package.

Examples

data(synthetic_clusters.int)

Pickup League Teams Interval Dataset

Description

Interval-valued data for 5 teams in a local pickup league, classified by season performance. Each team is described by ranges of player age, weight, and speed.

Usage

data(teams.int)

Format

A data frame with 5 observations and 7 columns (3 interval variables in _l/_u Min-Max pairs, plus a label):

• team_type: Performance category (Very Good, Good, Average, Fair, Poor).

• age_l, age_u: Player age range (years).

• weight_l, weight_u: Player weight range (pounds).

• speed_l, speed_u: Speed range – time to run 100 yards (seconds).

Details

The symbolic results are more informative than classical midpoint analyses: the Very Good team has homogeneous players, whereas the Poor team has players varying widely in age, weight, and speed. Used for symbolic principal component analysis.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.24, p.63.

Examples

data(teams.int)

World Cities Monthly Temperature Interval Dataset

Description

Interval-valued monthly temperatures for major cities worldwide. Benchmark dataset for comparing distance measures (Hausdorff, L2, Wasserstein) in dynamic clustering algorithms.

Usage

data(temperature_city.int)

Format

A data frame with 6 observations and 13 columns (6 monthly interval variables in _l/_u Min-Max pairs, plus a label). Only January through June are included:

• city: City name (character).

• jan_l, jan_u: January temperature range (degrees Celsius).

• feb_l, feb_u: February temperature range.

• mar_l, mar_u: March temperature range.

• apr_l, apr_u: April temperature range.

• may_l, may_u: May temperature range.

• jun_l, jun_u: June temperature range.

Details

Expert partition into 4 classes: Class 1 (tropical/warm), Class 2 (temperate European and Asian), Class 3 (Mauritius), Class 4 (Tehran).

Metadata

References

Verde, R. and Irpino, A. (2008). A new interval data distance based on the Wasserstein metric. Proc. COMPSTAT 2008, pp. 705-712.

Examples

data(temperature_city.int)

Tennis Court Types Interval Dataset

Description

Interval-valued data for tennis players aggregated by court type (Hard, Grass, Indoor, Clay) with weight, height, and racket tension.

Usage

data(tennis.int)

Format

A data frame with 4 observations and 7 columns (3 interval variables in _l/_u Min-Max pairs, plus a label):

• court_type: Type of court (Hard, Grass, Indoor, Clay).

• player_weight_l, player_weight_u: Player weight range (kg).

• player_height_l, player_height_u: Player height range (m).

• racket_tension_l, racket_tension_u: Racket tension range.

Details

Clustering on weight and height separates grass courts from the rest (decision rule: Weight <= 74.75 kg). When all three variables are used, clustering separates by racket tension instead.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.25, p.64.

Examples

data(tennis.int)

Convert Interval Data to All Supported Formats

Description

Convert interval data from any recognized format to all six supported interval data formats and return the results as a named list. This is useful for inspecting and comparing how the same interval data is represented across different formats.

Usage

to_all_interval_formats(x, ...)

Arguments

Details

Six interval data formats are supported in this package. Each format stores the same information – lower and upper bounds for every variable of every observation – but differs in its structure and origin:

RSDA

A symbolic_tbl object (class c("symbolic_tbl", "tbl_df", "tbl", "data.frame")) where each interval variable is a complex column (symbolic_interval): Re() gives the minimum and Im() gives the maximum. This is the native format of the RSDA package (Billard & Diday, 2006; Rodriguez, 2024).

MM (Min-Max)

A plain data.frame where each interval variable is represented by two numeric columns named <var>_min and <var>_max. This is a widely used general-purpose representation.

iGAP

A data.frame where each interval variable is stored as a character column with comma-separated values "min,max". This is the format used by the iGAP software (Correia, 2009).

ARRAY

A three-dimensional numeric array of size [n, p, 2]. The first slice [,,1] contains all minima and the second slice [,,2] contains all maxima. Dimnames encode observation labels, variable names, and c("min", "max"). This format is convenient for matrix-based computations.

SODAS

An XML file on disk produced by the SODAS software (Diday & Noirhomme, 2008). In R, SODAS data is referenced by its file path and read via RSDA::SODAS.to.RSDA(). Since SODAS is a file-based format, it cannot be generated from in-memory data.

SDS

An alias for SODAS. Both refer to the same XML-based format.

Value

A named list with six slots:

RSDA

A symbolic_tbl with complex-encoded symbolic_interval columns.

MM

A data.frame with paired _min/_max columns.

iGAP

A data.frame with comma-separated "min,max" character values.

ARRAY

A three-dimensional numeric array of dimension [n, p, 2] where [,,1] stores minima and [,,2] stores maxima.

SODAS

NULL unless the input is a SODAS XML file path, in which case it stores the original path.

SDS

NULL unless the input is a SODAS/SDS XML file path (alias for SODAS).

Author(s)

Han-Ming Wu

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley.

Rodriguez, O. (2024). RSDA: R to Symbolic Data Analysis. R package, https://CRAN.R-project.org/package=RSDA.

Correia, M. (2009). Interval GARCH and Aggregation of Predictions.

Diday, E. and Noirhomme-Fraiture, M. (2008). Symbolic Data Analysis and the SODAS Software. Wiley.

See Also

int_detect_format, int_convert_format, int_list_conversions

Examples

data(car.int)
result <- to_all_interval_formats(car.int)
names(result)

# RSDA format (symbolic_tbl)
result$RSDA

# MM format (data.frame with _min/_max columns)
head(result$MM)

# iGAP format (data.frame with comma-separated values)
head(result$iGAP)

# ARRAY format (3D array)
dim(result$ARRAY)
result$ARRAY[1:3, , 1]  # minima
result$ARRAY[1:3, , 2]  # maxima

# SODAS/SDS slots are NULL (file-based format)
result$SODAS
result$SDS

Town Services Concatenated Mixed Symbolic Dataset

Description

Symbolic data for 3 towns (Paris, Lyon, Toulouse) combining school and hospital databases. Contains interval-valued, multi-valued, and modal-valued variables.

Usage

data(town_services.mix)

Format

A data frame with 3 observations (Paris, Lyon, Toulouse) and 8 columns:

• town: Town name (character).

• no_pupils_l, no_pupils_u: Number of pupils range (Min-Max pair).

• type: School type (modal, character).

• level: Coded level (multi-valued, character).

• no_beds_l, no_beds_u: Number of beds range (Min-Max pair).

• specialty: Specialty code (multi-valued, character).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 1.21, p.19.

Examples

data(town_services.mix)

Trivial and Non-Trivial Intervals Example Dataset

Description

Simple 5x3 example illustrating different interval types: full intervals (hyperrectangles), degenerate intervals (lines), and trivial intervals (points). Used for vertices PCA demonstration.

Usage

data(trivial_intervals.int)

Format

A data frame with 5 observations (w1–w5) and 6 columns (3 interval variables in _l/_u Min-Max pairs):

• y1_l, y1_u: First interval variable.

• y2_l, y2_u: Second interval variable.

• y3_l, y3_u: Third interval variable.

Metadata