Package 'tensorsparse'

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

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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

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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

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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)

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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 [email protected]

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)

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