| Type: | Package |
| Title: | Multiway Clustering via Tensor Block Models |
| Version: | 3.0 |
| Date: | 2020-09-27 |
| Author: | Miaoyan Wang, Yuchen Zeng |
| Maintainer: | Yuchen Zeng <yzeng58@wisc.edu> |
| Imports: | parallel, stats |
| Suggests: | cluster |
| Description: | Implements the multiway sparse clustering approach of M. Wang and Y. Zeng, "Multiway clustering via tensor block models". Advances in Neural Information Processing System 32 (NeurIPS), 715-725, 2019. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | yes |
| Packaged: | 2020-09-27 18:27:15 UTC; cengyuchen |
| Repository: | CRAN |
| Date/Publication: | 2020-09-27 18:40:02 UTC |
| RoxygenNote: | 7.0.0 |
| Encoding: | UTF-8 |
Select the clustering size for order-3 sparse tensor clustering via BIC
Description
Select the clustering size for three-way clustering. The function searches over a range of clustering sizes and outputs the one that minimizes BIC. The clustering size (d_1, d_2, d_3) is a length-3 vector consisting of the number of clusters in each mode.
Usage
chooseClusteringSize(
x,
k,
r,
l,
lambda = 0,
sim.times = 1,
method = "L0",
n.cores = NULL
)
Arguments
x |
a three-dimensional array |
k |
a vector, the possible numbers of clusters at mode 1 |
r |
a vector, the possible numbers of clusters at mode 2 |
l |
a vector, the possible numbers of clusters at mode 3 |
lambda |
a numeric value, regularization coefficient |
sim.times |
the number of simulation replicates when performing clustering |
method |
two options: "L0", "L1". "L0" indicates L0 penalty, and "L1" indicates Lasso penalty |
n.cores |
the number of cores in parallel implementation |
Value
a list
estimated_krl a 1*3 matrix consisting of the estimated clustering size
BIC a vector consisting of the BIC value for all combinations of clustering sizes
Select the regularization coefficient for order-3 sparse tensor clustering via BIC
Description
Select the regularization coefficient for three-way clustering. The clustering size is assumed to be known. The function searches over a range of regularization sizes and outputs the one that minimizes the BIC.
Usage
chooseLambda(x, k, r, l, lambda = NULL, method = "L0")
Arguments
x |
a three-dimensional array |
k |
an positive integer, the numbers of clusters at mode 1 |
r |
an positive integer, the numbers of clusters at mode 2 |
l |
an positive integer, the numbers of clusters at mode 3 |
lambda |
a vector of possible lambda, eg: lambda = c(0,50,100,200) |
method |
two options: "L0", "L1". "L0" indicates L0 penalty, and "L1" indicates Lasso penalty |
Value
a list
lambda the lambda with lowest BIC
BIC the BIC for each lambda in the given range
nonzeromus the number of clusters with non-zero means
Generate a random order-3 tensor
Description
Generate an order-3 random tensor based on tensor block model.
Usage
getOrder3Tensor(
n,
p,
q,
k = NULL,
r = NULL,
l = NULL,
error = 3,
sort = TRUE,
sparse.percent = 0,
center = FALSE,
seed = NULL,
mumin = -3,
mumax = 3
)
Arguments
n |
the dimension at mode 1 |
p |
the dimension at mode 2 |
q |
the dimension at mode 3 |
k |
an positive integer, the numbers of clusters at mode 1 |
r |
an positive integer, the numbers of clusters at mode 2 |
l |
an positive integer, the numbers of clusters at mode 3 |
error |
a positive numeric value, noise level |
sort |
if TRUE, the tensor entries belonging to the same cluster would be assumed together |
sparse.percent |
the proportion of zero entries based on the Gaussian tensor block model |
center |
if True, the data tensor would be centered to zero-mean before clustering |
seed |
a positive integer, used to specify the random seed |
mumin |
a numeric value, the lower bound of the block mean |
mumax |
a numeric value, the upper bound of the block mean |
Value
a list
x the tensor
truthX the underlying signal tensor following block model
truthCs true cluster label assignment at mode 1
truthDs true cluster label assignment at mode 2
truthEs true cluster label assignment at mode 3
mus the block means
binaryX the 0-1 tensor (0:the mean signal = 0; 1:the mean signal != 0)
Examples
getOrder3Tensor(20,20,20,2,2,2)$x
Generate a random order-4 tensor
Description
Generate a random order-4 tensor based on tensor block model.
Usage
getOrder4Tensor(
n,
p,
q,
s,
k = NULL,
r = NULL,
l = NULL,
m = NULL,
error = 3,
sort = TRUE,
sparse.percent = 0,
center = FALSE,
seed = NULL,
mumin = -3,
mumax = 3
)
Arguments
n |
the dimension at mode 1 |
p |
the dimension at mode 2 |
q |
the dimension at mode 3 |
s |
the dimension at mode 4 |
k |
an positive integer, the numbers of clusters at mode 1 |
r |
an positive integer, the numbers of clusters at mode 2 |
l |
an positive integer, the numbers of clusters at mode 3 |
m |
an positive integer, the numbers of clusters at mode 4 |
error |
a positive numeric value, noise level |
sort |
if TRUE, the tensor entries belonging to the same cluster would be assumed together |
sparse.percent |
the proportion of zero entries based on the Gaussian tensor block model |
center |
if True, the data tensor would be centered to zero-mean before clustering |
seed |
a positive integer, used to specify the random seed |
mumin |
a numeric value, the lower bound of the block mean |
mumax |
a numeric value, the upper bound of the block mean |
Value
a list
x the tensor
truthX the underlying signal tensor following block model
truthCs true cluster label assignment at mode 1
truthDs true cluster label assignment at mode 2
truthEs true cluster label assignment at mode 3
truthFs true cluster label assignment at mode 4
mus the block means
binaryX the 0-1 tensor (0:the mean signal = 0; 1:the mean signal != 0)
Examples
getOrder4Tensor(10,10,10,10,2,2,2,2)
Perform tensor clustering via tensor block model (TBM)
Description
Perform tensor clustering via tensor block model (TBM) method.
Usage
tbmClustering(
x,
k,
r,
l,
lambda = 0,
max.iter = 1000,
threshold = 1e-10,
sim.times = 1,
trace = FALSE,
Cs.init = NULL,
Ds.init = NULL,
Es.init = NULL,
method = "L0"
)
Arguments
x |
an order-3 data tensor |
k |
an positive integer, the numbers of clusters at mode 1 |
r |
an positive integer, the numbers of clusters at mode 2 |
l |
an positive integer, the numbers of clusters at mode 3 |
lambda |
a numeric value, regularization coefficient |
max.iter |
a positive integer, the maximum numbers of iteration |
threshold |
a positive small numeric value for convergence threshold |
sim.times |
the number of simulation replicates when performing clustering |
trace |
logic value, print result per each iteration if TRUE |
Cs.init |
vector or NULL, initial cluster label assignment at mode 1 |
Ds.init |
vector or NULL, initial cluster label assignment at mode 2 |
Es.init |
vector or NULL, initial cluster label assignment at mode 3 |
method |
two options: "L0", "L1". "L0" indicates L0 penalty, and "L1" indicates Lasso penalty |
Value
a list
judgeX estimated underlying signal tensor
Cs clustering result at mode 1
Ds clustering result at mode 2
Es clustering result at mode 3
mus estimated block means
Author(s)
Yuchen Zeng yzeng58@wisc.edu
References
M. Wang and Y. Zeng, "Multiway clustering via tensoe block models". Advances in Neural Information Processing System 32 (NeurIPS), 715-725, 2019.
Examples
x = getOrder3Tensor(20,20,20,2,2,2)$x
tbmClustering(x,2,2,2)