Package 'iTensor'

Title: ICA-Based Matrix/Tensor Decomposition
Description: Some functions for performing ICA, MICA, Group ICA, and Multilinear ICA are implemented. ICA, MICA/Group ICA, and Multilinear ICA extract statistically independent components from single matrix, multiple matrices, and single tensor, respectively. For the details of these methods, see the reference section of GitHub README.md <https://github.com/rikenbit/iTensor>.
Authors: Koki Tsuyuzaki [aut, cre]
Maintainer: Koki Tsuyuzaki <[email protected]>
License: MIT + file LICENSE
Version: 1.0.3
Built: 2025-03-03 05:05:44 UTC
Source: https://github.com/rikenbit/itensor

Help Index

CorrIndex

Description

Calculate the CorrIndex of the cross-correlation matrix of S_true and estimated S. The closer the value is to 0, the closer estimated S is to S_true.

Usage

CorrIndex(cross_correlation_matrix)

Arguments

cross_correlation_matrix

Cross-correlation matrix

Value

CorrIndex, which means the closeness between S and S_true , is returned.

Examples

S_true <- matrix(runif(5*5), nrow=5, ncol=5)
S <- matrix(runif(5*5), nrow=5, ncol=5)
CorrIndex(cor(S_true, S))

Group Independent Component Analysis (GroupICA)

Description

The input data is assumed to be a list containing multiple matrices, which share common column.

Usage

GroupICA(
  Xs,
  J1,
  J2 = J1,
  algorithm = c("pooled", "Calhoun2009", "Pfister2018"),
  ica.algorithm = c("FastICA", "InfoMax", "ExtInfoMax", "JADE", "AuxICA1", "AuxICA2",
    "IPCA", "SIMBEC", "AMUSE", "SOBI", "FOBI", "ProDenICA", "RICA"),
  num.iter = 30,
  thr = 1e-10,
  verbose = FALSE
)

Arguments

Xs

A list containing multiple matrices
J1

Rank parameter to decompose
J2

Rank parameter used in Calhoun2009
algorithm

Pool algorithm to merge multiple ICA results (Default: pooled)
ica.algorithm

The decomposition algorithm (Default: "FastICA")
num.iter

The number of iterations
thr

The threshold to terminate the iteration (Default: 1E-10)
verbose

Verbose option

Value

A list containing the result of the decomposition

Examples

X1 <- matrix(runif(100*200), nrow=100, ncol=200)
X2 <- matrix(runif(150*200), nrow=150, ncol=200)
Xs <- list(X1=X1, X2=X2)
out <- GroupICA(Xs, J1=5)

Independent Component Analysis (Classic Methods)

Description

The input data is assumed to be a matrix. ICA decomposes the matrix and extract the components that are statistically independent each other.

Usage

ICA(
  X,
  J,
  algorithm = c("FastICA", "InfoMax", "ExtInfoMax"),
  num.iter = 100,
  thr = 1e-10,
  nonlinear_func = c("tanh", "exp", "kurtosis"),
  learning_rate = 1,
  verbose = FALSE
)

Arguments

X

A matrix
J

Rank parameter to decompose
algorithm

The decomposition algorithm (Default: "FastICA")
num.iter

The number of iteration
thr

The threshold to terminate the iteration (Default: 1E-10)
nonlinear_func

The function used in FastICA (Default: "tanh")
learning_rate

The learning rate used in InfoMax or ExtInfoMax
verbose

Verbose option

Value

A list containing the result of the decomposition

Examples

X <- matrix(runif(100*200), nrow=100, ncol=200)
J <- 5
out.FastICA <- ICA(X, J=J, algorithm="FastICA")
out.InfoMax <- ICA(X, J=J, algorithm="InfoMax")
out.ExtInfoMax <- ICA(X, J=J, algorithm="ExtInfoMax")

Independent Component Analysis (Modern Methods)

Description

The input data is assumed to be a matrix. ICA decomposes the matrix and extract the components that are statistically independent each other.

Usage

ICA2(
  X,
  J,
  algorithm = c("JADE", "AuxICA1", "AuxICA2", "IPCA", "SIMBEC", "AMUSE", "SOBI", "FOBI",
    "ProDenICA", "RICA"),
  num.iter = NULL,
  thr = 1e-10,
  r_list = NULL,
  omega_for_each_r = NULL,
  a_r_for_each_r = NULL,
  tau_list = NULL,
  num_bins = NULL,
  alpha = NULL,
  num_epoch = NULL,
  verbose = FALSE
)

Arguments

X

A matrix
J

Rank parameter to decompose
algorithm

The decomposition algorithm (Default: "JADE")
num.iter

The number of iteration
thr

The threshold to terminate the iteration (Default: 1E-10)
r_list

List of r-th order cumulants used in SIMBEC (Default: NULL)
omega_for_each_r

Weight vector of r_list used in SIMBEC (Default: NULL)
a_r_for_each_r

Parameter vector to specify the shape of partial activation function in SIMBEC (Default: NULL)
tau_list

List of lags to consider the auto-correlation used in AMUSE and SOBI (Default: NULL)
num_bins

Number of bins for histgram in ProDenICA (Default: NULL)
alpha

Learning rate used for gradient descent in RICA (Default: NULL)
num_epoch

Number of epoch used for gradient descent in RICA (Default: NULL)
verbose

Verbose option

Value

A list containing the result of the decomposition

Examples

ICA2

Multimodal independent component analysis

Description

The input datasets are assumed to be two matrices sharing the column space. MICA decomposes the matrices simutanously and extracts the components that maximizes the mutual information between the components.

Usage

MICA(
  X,
  Y,
  J,
  eta = 1000 * 1e-04,
  verbose = FALSE,
  mu = 50 * 1e-04,
  gamma_ts = 1
)

Arguments

X

A matrix sharing the column space with Y (??? x N)
Y

A matrix sharing the column space with X (??? x N)
J

The rank parameter to decompose the matrices
eta

A learning rate parameter of stochastic gradient descent
verbose

Verbose option
mu

A learning rate parameter of stochastic gradient descent
gamma_ts

Weighting factor for dependence on independence

Value

A list containing the result of the decomposition

Examples

X <- array(runif(10*20), dim=c(10,20))
Y <- array(runif(15*20), dim=c(15,20))
J <- 20
out <- MICA(X, Y, J=J)

Multilinear independent component analysis

Description

#' The input object is assumed to be a Tensor object defined by rTensor package. In MultilinearICA, ICA function is performed in each mode of the tensor.

Usage

MultilinearICA(
  X,
  Js = c(3, 3, 3),
  modes = 1:3,
  algorithm = c("FastICA", "InfoMax", "ExtInfoMax")
)

Arguments

X

An rTensor object
Js

A vector to specify the rank in each mode (Default: c(3,3,3))
modes

A vector to specify which modes are decomposed (Default: 1:3)
algorithm

The algorithm to decompose the input tensor in each mode (Default: "FastICA")

Value

A list containing the result of the decomposition

Examples

library("rTensor")
arrX <- array(runif(10*20*30), dim=c(10,20,30))
X <- as.tensor(arrX)
Js <- c(2,3,4)
out <- MultilinearICA(X, Js=Js)

Toy model data for using ICA, MICA, and GroupICA There are 7 types of simulation: ICA_Type1: Time-independent sub-gaussian data ICA_Type2: Time-independent super-gaussian data ICA_Type3: Data mixed with signals having no time dependence and different kurtosis ICA_Type4: Time-dependent data ICA_Type5: Toydata to model IPCA in N < P systems MICA: Two time-serices data to model MICA GroupICA: Toydata to model GroupICA

Description

Toy model data for using ICA, MICA, and GroupICA There are 7 types of simulation: ICA_Type1: Time-independent sub-gaussian data ICA_Type2: Time-independent super-gaussian data ICA_Type3: Data mixed with signals having no time dependence and different kurtosis ICA_Type4: Time-dependent data ICA_Type5: Toydata to model IPCA in N < P systems MICA: Two time-serices data to model MICA GroupICA: Toydata to model GroupICA

Usage

toyModel(model = "ICA_Type1", seeds = 123)

Arguments

model

"ICA_Type1", "ICA_Type2", "ICA_Type3", "ICA_Type4", and "ICA_Type5", "MICA", and "GrouICA" are available (Default: "ICA_Type1").
seeds

Random number for setting set.seeds in the function (Default: 123).

Value

A list containing simulation data sets.

Examples

data1 <- toyModel("ICA_Type1")
data2 <- toyModel("ICA_Type2")
data3 <- toyModel("ICA_Type3")
data4 <- toyModel("ICA_Type4")
data5 <- toyModel("ICA_Type5")
data6 <- toyModel("MICA")
data7 <- toyModel("GroupICA")