| Type: | Package |
| Title: | ICA-Based Matrix/Tensor Decomposition |
| Version: | 1.0.2 |
| 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. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| Depends: | R (≥ 4.1.0) |
| URL: | https://github.com/rikenbit/iTensor |
| RoxygenNote: | 7.2.3 |
| Suggests: | nnTensor, knitr, rmarkdown, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| Imports: | MASS, methods, graphics, utils, stats, rTensor, jointDiag, mgcv, einsum, geigen, mixOmics, groupICA |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2023-04-28 06:56:13 UTC; root |
| Author: | Koki Tsuyuzaki [aut, cre] |
| Maintainer: | Koki Tsuyuzaki <k.t.the-answer@hotmail.co.jp> |
| Repository: | CRAN |
| Date/Publication: | 2023-04-28 08:00:02 UTC |
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", "JADE", "AuxICA1", "AuxICA2", "IPCA",
"SIMBEC", "AMUSE", "SOBI", "FOBI", "ProDenICA", "RICA")
)
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")