Repository Mirror for your Cloud Server and Webhosting

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)