Package 'SparseICA'

Title: Sparse Independent Component Analysis
Description: Provides an implementation of the Sparse ICA method in Wang et al. (2024) <doi:10.1080/01621459.2024.2370593> for estimating sparse independent source components of cortical surface functional MRI data, by addressing a non-smooth, non-convex optimization problem through the relax-and-split framework. This method effectively balances statistical independence and sparsity while maintaining computational efficiency.
Authors: Zihang Wang [aut, cre] , Irina Gaynanova [aut] , Aleksandr Aravkin [aut] , Benjamin Risk [aut]
Maintainer: Zihang Wang <[email protected]>
License: GPL-3
Version: 0.1.4
Built: 2025-01-29 20:33:15 UTC
Source: CRAN

Help Index

BIC-like Criterion for Tuning Parameter Selection in Sparse ICA

Description

This function uses a BIC-like criterion to select the optimal tuning parameter nu for Sparse ICA.

Usage

BIC_sparseICA(
  xData,
  n.comp,
  nu_list = seq(0.1, 4, 0.1),
  whiten = c("eigenvec", "sqrtprec", "none"),
  lngca = FALSE,
  orth.method = c("svd", "givens"),
  method = c("C", "R"),
  use_irlba = TRUE,
  eps = 1e-06,
  maxit = 500,
  verbose = FALSE,
  col.stand = TRUE,
  row.stand = FALSE,
  iter.stand = 0,
  BIC_plot = FALSE
)

Arguments

xData

A numeric matrix of input data with dimensions P x T, where P is the number of features and T is the number of samples.
n.comp

An integer specifying the number of components to estimate.
nu_list

A numeric vector specifying the list of candidate tuning parameters. Default is seq(0.1, 4, 0.1).
whiten

A character string specifying the method for whitening the input xData. Options are "eigenvec", "sqrtprec", or "none". Default is "eigenvec".
lngca

A logical value indicating whether to perform Linear Non-Gaussian Component Analysis (LNGCA). Default is FALSE.
orth.method

A character string specifying the method for generating initial values of the U matrix. Default is "svd".
method

A character string specifying the computation method. If "C" (default), C code is used for Sparse ICA to improve performance. If "R", computations are performed entirely in R.
use_irlba

A logical value indicating whether to use the irlba method for fast truncated Singular Value Decomposition (SVD) during whitening. This can improve memory efficiency for intermediate datasets. Default is TRUE.
eps

A numeric value specifying the convergence threshold. Default is 1e-6.
maxit

An integer specifying the maximum number of iterations for the Sparse ICA method using Laplace density. Default is 500.
verbose

A logical value indicating whether to print convergence information during execution. Default is FALSE.
col.stand

A logical value indicating whether to standardize columns. For each column, the mean of the entries in the column equals 0, and the variance of the entries in the column equals 1. Default is TRUE.
row.stand

A logical value indicating whether to standardize rows. For each row, the mean of the entries in the row equals 0, and the variance of the entries in the row equals 1. Default is FALSE.
iter.stand

An integer specifying the number of iterations for achieving both row and column standardization when col.stand = TRUE and row.stand = TRUE. Default is 5.
BIC_plot

A logical value indicating whether to generate a plot showing the trace of BIC values for different nu candidates. Default is FALSE.

Value

A list containing the following elements:

BIC

A numeric vector of BIC values corresponding to each candidate nu in nu_list.

nu_list

A numeric vector of candidate tuning parameter values.

best_nu

The optimal nu selected based on the BIC-like criterion.

Examples

#get simulated data
data(example_sim123)

select_sparseICA = BIC_sparseICA(xData = example_sim123$xmat, n.comp = 3, 
      method="C", BIC_plot = TRUE,verbose = TRUE, nu_list = seq(0.1,4,0.1))

(my_nu = select_sparseICA$best_nu)

Create a List of fMRI Files for Group ICA Analysis

Description

This function scans a BIDS-formatted directory for subject-specific fMRI files that match a specified pattern and returns a list of these files for use in group ICA analysis.

Usage

create_group_list(bids_path, pattern = "task-rest.*\\.dtseries\\.nii$")

Arguments

bids_path

A character string specifying the path to the root directory of the BIDS-formatted dataset. This directory should contain subject folders (e.g., sub-*).
pattern

A character string specifying the pattern to match fMRI files. The default is "task-rest.*\.dtseries\.nii$".

Value

A named list where each element corresponds to a subject directory and contains a vector of matched fMRI file paths. The names of the list are the subject IDs.

Examples

# Example usage:
# Assuming `bids_dir` is the path to a BIDS dataset:
# group_list <- create_group_list(bids_path = bids_dir, pattern = "task-rest.*\.dtseries\.nii$")
# Print the structure of the list:
# str(group_list)

Estimate mixing matrix from estimates of components

Description

Estimate mixing matrix from estimates of components

Usage

est.M.ols(sData, xData, intercept = TRUE)

Arguments

sData

S Dimension: P x Q
xData

X Dimension: P x T
intercept

default = TRUE

Value

a mixing matrix M, dimension Q x T.

Example sim123 Dataset

Description

A simple dataset for demonstration purposes.

Usage

example_sim123

Format

A list containing 3 data frames:

smat

A 1089 x 3 numeric matrix of the true source signals. Each column is an 33 x 33 image.

mmat

A 3 x 50 numeric mixing matrix of the true time series. Each row is a time series of corresponding column in smat.

xmat

A 1089 x 50 numeric matrix of the simulated data. Each column is the simulated mixed signal at a time point.

Examples

data(example_sim123)
str(example_sim123)

Generate Group-Level Principal Components (PCs) for fMRI Data

Description

This function computes subject-level principal components (PCs) from fMRI data and performs a group-level PCA for dimension reduction, designed for cortical surface fMRI data in BIDS format.

Usage

gen_groupPC(
  bids_path,
  subj_list,
  n.comp = 30,
  ncore = 1,
  npc = 85,
  iter_std = 5,
  brainstructures = c("left", "right"),
  verbose = TRUE
)

Arguments

bids_path

A character string specifying the root directory of the BIDS-formatted dataset.
subj_list

A named list generated from create_group_list containing fMRI file paths for each subject.
n.comp

An integer specifying the number of components to retain during group-level PCA. Default is 30.
ncore

An integer specifying the number of cores to use for parallel processing. Default is 1.
npc

An integer specifying the number of components to retain during subject-level PCA. Default is 85.
iter_std

An integer specifying the number of iterative standardization steps to apply to fMRI data. Default is 5.
brainstructures

A character vector specifying the brain structures to include in the analysis. Options are "left" (left cortex), "right" (right cortex), and/or "subcortical" (subcortex and cerebellum). Can also be "all" (obtain all three brain structures). Default is c("left", "right").
verbose

A logical value indicating whether to print convergence information during execution. Default is TRUE.

Details

NOTE: This function requires the ciftiTools package to be installed, and set up the path to the Connectome Workbench folder by ciftiTools.setOption(). See the package ciftiTools documentation for more information.

Value

A numeric matrix containing the group-level principal components, with dimensions determined by the number of retained components (n.comp) and the concatenated data across all subjects.

Function for generating random starting points

Description

Function for generating random starting points

Usage

gen.inits(p, d, runs, orth.method = c("svd", "givens"))

Arguments

p

The number of rows.
d

The number of columns.
runs

The number of random starts.
orth.method

The method used for generating initial values of U matrix. The default is "svd".

Value

A list of random initialization of matrices.

For a given angle theta, returns a d x d Givens rotation matrix

Description

For a given angle theta, returns a d x d Givens rotation matrix

Usage

givens.rotation(theta = 0, d = 2, which = c(1, 2))

Arguments

theta

The value of theta.
d

The value of d.
which

The value of which.

Perform Group Sparse Independent Component Analysis (Sparse ICA)

Description

This function performs Sparse ICA on group-level fMRI data. It processes BIDS-formatted fMRI datasets, performs PCA to reduce dimensionality, selects a tuning parameter nu (optionally using a BIC-like criterion), and executes Sparse ICA to estimate independent components.

Usage

group_sparseICA(
  bids_path,
  subj_list = NULL,
  nu = "BIC",
  n.comp = 30,
  method = "C",
  ncore = 1,
  npc = 85,
  iter_std = 5,
  brainstructures = c("left", "right"),
  restarts = 40,
  positive_skewness = TRUE,
  use_irlba = TRUE,
  eps = 1e-06,
  maxit = 500,
  BIC_plot = TRUE,
  nu_list = seq(0.1, 4, 0.05),
  verbose = TRUE,
  BIC_verbose = FALSE,
  converge_plot = FALSE
)

Arguments

bids_path

A character string specifying the root directory of the BIDS-formatted dataset.
subj_list

A named list where each element corresponds to a subject and contains vectors of fMRI file names. If NULL, the subject list is generated automatically using create_group_list. Default is NULL.
nu

A numeric value for the tuning parameter, or "BIC" to select nu using a BIC-like criterion. Default is "BIC".
n.comp

An integer specifying the number of components to estimate. Default is 30.
method

A character string specifying the computation method for Sparse ICA. Options are "C" (default) for C-based computation or "R" for R-based computation.
ncore

An integer specifying the number of cores to use for parallel processing. Default is 1.
npc

An integer specifying the number of components to retain during subject-level PCA. Default is 85.
iter_std

An integer specifying the number of iterative standardization steps to apply to fMRI data. Default is 5.
brainstructures

A character vector specifying the brain structures to include in the analysis. Options are "left" (left cortex), "right" (right cortex), and/or "subcortical" (subcortex and cerebellum). Can also be "all" (obtain all three brain structures). Default is c("left", "right").
restarts

An integer specifying the number of random initializations for Sparse ICA. Default is 40.
positive_skewness

A logical value indicating whether to enforce positive skewness on the estimated components. Default is TRUE.
use_irlba

A logical value indicating whether to use the irlba method for fast truncated Singular Value Decomposition (SVD) during whitening. This can improve memory efficiency for intermediate datasets. Default is TRUE.
eps

A numeric value specifying the convergence threshold. Default is 1e-6.
maxit

An integer specifying the maximum number of iterations for Sparse ICA. Default is 500.
BIC_plot

A logical value indicating whether to generate a plot of BIC values for different nu candidates when selecting nu. Default is TRUE.
nu_list

A numeric vector specifying candidate values for nu when selecting it using a BIC-like criterion. Default is seq(0.1, 4, 0.05).
verbose

A logical value indicating whether to print progress messages. Default is TRUE.
BIC_verbose

A logical value indicating whether to print detailed messages during the BIC-based selection of nu. Default is FALSE.
converge_plot

A logical value indicating whether to generate a plot showing the convergence trace during Sparse ICA. Default is FALSE.

Details

The function operates in four main steps:

  1. If subj_list is not provided, it creates a list of subject-specific fMRI files using create_group_list.

  2. Performs subject-level PCA using gen_groupPC to reduce data dimensionality.

  3. Selects the tuning parameter nu using a BIC-like criterion (if nu = "BIC") or uses the provided nu.

  4. Executes Sparse ICA on the group-level PCs to estimate independent components.

Value

A list containing the results of the group Sparse ICA analysis, including:

loglik

The minimal log-likelihood value among the random initializations.

estS

A numeric matrix of estimated sparse independent components with dimensions P x Q.

estU

The estimated U matrix with dimensions Q x Q.

whitener

The whitener matrix used for data whitening.

converge

The trace of convergence for the U matrix.

best_nu

The selected nu value (if nu = "BIC").

BIC

A numeric vector of BIC values for each nu candidate (if nu = "BIC").

nu_list

The list of nu candidates used in the BIC-based selection (if nu = "BIC").

See Also

create_group_list, gen_groupPC, BIC_sparseICA, sparseICA

Match ICA results based on L2 distances and Hungarian

Description

Match ICA results based on L2 distances and Hungarian

Usage

matchICA(S, template, M = NULL)

Arguments

S

loading variable matrix
template

template for match
M

subject score matrix

Value

the match result

Relax-and-split ICA Function for Sparse ICA wrapper

Description

This function performs Sparse Independent Component Analysis (Sparse ICA), implemented in both pure R and RCpp for efficiency.

Usage

relax_and_split_ICA(
  xData,
  n.comp,
  nu = 1,
  U.list = NULL,
  whiten = c("eigenvec", "sqrtprec", "none"),
  lngca = FALSE,
  orth.method = c("svd", "givens"),
  method = c("C", "R"),
  restarts = 40,
  use_irlba = TRUE,
  eps = 1e-06,
  maxit = 500,
  verbose = FALSE,
  converge_plot = FALSE,
  col.stand = TRUE,
  row.stand = FALSE,
  iter.stand = 5,
  positive_skewness = TRUE
)

Arguments

xData

A numeric matrix of input data with dimensions P x T, where P is the number of features and T is the number of samples.
n.comp

An integer specifying the number of components to estimate.
nu

A numeric tuning parameter controlling the balance between accuracy and sparsity of the results. It can be selected using a BIC-like criterion or based on expert knowledge. Default is 1.
U.list

An optional matrix specifying the initialization of the U matrix. Default is NULL.
whiten

A character string specifying the method for whitening the input xData. Options are "eigenvec", "sqrtprec", "lngca", or "none". Default is "eigenvec".
lngca

A logical value indicating whether to perform Linear Non-Gaussian Component Analysis (LNGCA). Default is FALSE.
orth.method

A character string specifying the method used for generating initial values for the U matrix. Default is "svd".
method

A character string specifying the computation method. If "C" (default), C code is used for most computations for better performance. If "R", computations are performed entirely in R.
restarts

An integer specifying the number of random initializations for optimization. Default is 40.
use_irlba

A logical value indicating whether to use the irlba method for fast truncated Singular Value Decomposition (SVD) during whitening. This can improve memory efficiency for intermediate datasets. Default is TRUE.
eps

A numeric value specifying the convergence threshold. Default is 1e-6.
maxit

An integer specifying the maximum number of iterations for the Sparse ICA method using Laplace density. Default is 500.
verbose

A logical value indicating whether to print convergence information during execution. Default is FALSE.
converge_plot

A logical value indicating whether to generate a line plot showing the convergence trace. Default is FALSE.
col.stand

A logical value indicating whether to standardize columns. For each column, the mean of the entries in the column equals 0, and the variance of the entries in the column equals 1. Default is TRUE.
row.stand

A logical value indicating whether to standardize rows. For each row, the mean of the entries in the row equals 0, and the variance of the entries in the row equals 1. Default is FALSE.
iter.stand

An integer specifying the number of iterations for achieving both row and column standardization when col.stand = TRUE and row.stand = TRUE. Default is 5.
positive_skewness

A logical value indicating whether to enforce positive skewness on the estimated components. Default is TRUE.

Value

A list containing the following elements:

loglik

The minimal log-likelihood value among the random initializations.

estS

A numeric matrix of estimated sparse independent components with dimensions P x Q.

estU

The estimated U matrix with dimensions Q x Q.

estM

The estimated mixing matrix with dimensions Q x T.

whitener

The whitener matrix used for data whitening.

converge

Convergence information for the U matrix.

Change the sign of S and M matrices to positive skewness.

Description

Change the sign of S and M matrices to positive skewness.

Usage

signchange(S, M = NULL)

Arguments

S

The S matrix with dimension P x Q.
M

The M matrix with dimension Q x T.

Value

A list of S and M matrices with positive skewness.

Soft-threshold function

Description

Soft-threshold function

Usage

soft_thresh_R(x, nu = 1, lambda = sqrt(2)/2)

Arguments

x

The input scalar.
nu

The tuning parameter.
lambda

The lambda parameter of the Laplace density.

Sparse Independent Component Analysis (Sparse ICA) Function

Description

This function performs Sparse Independent Component Analysis (Sparse ICA), implemented in both pure R and RCpp for efficiency.

Usage

sparseICA(
  xData,
  n.comp,
  nu = "BIC",
  nu_list = seq(0.1, 4, 0.1),
  U.list = NULL,
  whiten = c("eigenvec", "sqrtprec", "none"),
  lngca = FALSE,
  orth.method = c("svd", "givens"),
  method = c("C", "R"),
  restarts = 40,
  use_irlba = TRUE,
  eps = 1e-06,
  maxit = 500,
  verbose = TRUE,
  BIC_verbose = FALSE,
  converge_plot = FALSE,
  col.stand = TRUE,
  row.stand = FALSE,
  iter.stand = 5,
  positive_skewness = TRUE
)

Arguments

xData

A numeric matrix of input data with dimensions P x T, where P is the number of features and T is the number of samples.
n.comp

An integer specifying the number of components to estimate.
nu

A positive numeric value or a character "BIC" specifying the tuning parameter controlling the balance between accuracy and sparsity of the results. It can be selected using a BIC-like criterion ("BIC") or based on expert knowledge (a positive number). Default is "BIC".
nu_list

A numeric vector specifying the list of candidate tuning parameters. Default is seq(0.1, 4, 0.1).
U.list

An optional matrix specifying the initialization of the U matrix. Default is NULL.
whiten

A character string specifying the method for whitening the input xData. Options are "eigenvec", "sqrtprec", "lngca", or "none". Default is "eigenvec".
lngca

A logical value indicating whether to perform Linear Non-Gaussian Component Analysis (LNGCA). Default is FALSE.
orth.method

A character string specifying the method used for generating initial values for the U matrix. Default is "svd".
method

A character string specifying the computation method. If "C" (default), C code is used for most computations for better performance. If "R", computations are performed entirely in R.
restarts

An integer specifying the number of random initializations for optimization. Default is 40.
use_irlba

A logical value indicating whether to use the irlba method for fast truncated Singular Value Decomposition (SVD) during whitening. This can improve memory efficiency for intermediate datasets. Default is TRUE.
eps

A numeric value specifying the convergence threshold. Default is 1e-6.
maxit

An integer specifying the maximum number of iterations for the Sparse ICA method using Laplace density. Default is 500.
verbose

A logical value indicating whether to print convergence information during execution. Default is TRUE.
BIC_verbose

A logical value indicating whether to print BIC selection information. Default is FALSE.
converge_plot

A logical value indicating whether to generate a line plot showing the convergence trace. Default is FALSE.
col.stand

A logical value indicating whether to standardize columns. For each column, the mean of the entries in the column equals 0, and the variance of the entries in the column equals 1. Default is TRUE.
row.stand

A logical value indicating whether to standardize rows. For each row, the mean of the entries in the row equals 0, and the variance of the entries in the row equals 1. Default is FALSE.
iter.stand

An integer specifying the number of iterations for achieving both row and column standardization when col.stand = TRUE and row.stand = TRUE. Default is 5.
positive_skewness

A logical value indicating whether to enforce positive skewness on the estimated components. Default is TRUE.

Value

A list containing the following elements:

loglik

The minimal log-likelihood value among the random initializations.

estS

A numeric matrix of estimated sparse independent components with dimensions P x Q.

estM

The estimated mixing matrix with dimensions Q x T.

estU

The estimated U matrix with dimensions Q x Q.

whitener

The whitener matrix used for data whitening.

converge

The trace of convergence for the U matrix.

BIC

A numeric vector of BIC values corresponding to each candidate nu in nu_list.

nu_list

A numeric vector of candidate tuning parameter values.

best_nu

The optimal nu selected based on the BIC-like criterion.

Examples

#get simulated data
data(example_sim123)

my_sparseICA <- sparseICA(xData = example_sim123$xmat, n.comp = 3, nu = "BIC", method="C",
      restarts = 40, eps = 1e-6, maxit = 500, verbose=TRUE)

res_matched <- matchICA(my_sparseICA$estS,example_sim123$smat)

# Visualize the estimated components
oldpar <- par()$mfrow
par(mfrow=c(1,3))
image(matrix(res_matched[,1],33,33))
image(matrix(res_matched[,2],33,33))
image(matrix(res_matched[,3],33,33))
par(mfrow=oldpar)

Convert angle vector into orthodox matrix

Description

Convert angle vector into orthodox matrix

Usage

theta2W(theta)

Arguments

theta

A vector of angles theta.

Value

An orthodox matrix.

The function for perform whitening.

Description

The function for perform whitening.

Usage

whitener(X, n.comp = ncol(X), center.row = FALSE, use_irlba = TRUE)

Arguments

X

The data matrix with dimension P x T.
n.comp

The number of components.
center.row

Whether to center the row of data. Default is FALSE.
use_irlba

Whether to use the irlba method to perform fast truncated singular value decomposition in whitening step, helpful for memorying intermediate dataset. Default is TRUE.

Value

A list including the whitener matrix, the whitened data matrix, and the mean of the input data.