Title: Independent Component Analysis for Grouped Data
Version: 0.1.1
Author: Niklas Pfister and Sebastian Weichwald
Maintainer: Niklas Pfister <pfister@stat.math.ethz.ch>
Description: Contains an implementation of an independent component analysis (ICA) for grouped data. The main function groupICA() performs a blind source separation, by maximizing an independence across sources and allows to adjust for varying confounding for user-specified groups. Additionally, the package contains the function uwedge() which can be used to approximately jointly diagonalize a list of matrices. For more details see the project website https://sweichwald.de/groupICA/.
URL: https://github.com/sweichwald/groupICA-R
BugReports: https://github.com/sweichwald/groupICA-R/issues
Depends: R (≥ 3.2.3)
License: AGPL-3
Encoding: UTF-8
LazyData: true
Imports: stats, MASS
RoxygenNote: 6.0.1
NeedsCompilation: no
Packaged: 2018-06-06 11:57:47 UTC; pfisteni
Repository: CRAN
Date/Publication: 2018-06-19 08:55:29 UTC

groupICA

Description

Estimates the unmixing and confounded sources of the groupICA model X=A(S+H).

Usage

groupICA(X, group_index = NA, partition_index = NA, n_components = NA,
  n_components_uwedge = NA, rank_components = FALSE,
  pairing = "complement", groupsize = 1, partitionsize = NA,
  max_iter = 1000, tol = 1e-12, silent = TRUE)

Arguments

X

data matrix. Each column corresponds to one predictor variable.

group_index

vector coding to which group each sample belongs, with length(group_index)=nrow(X). If no group index is provided a rigid grid with groupsize samples per group is used (which defaults to all samples if groupsize was not set).

partition_index

vector coding to which partition each sample belongs, with length(partition_index)=nrow(X). If no partition index is provided a rigid grid with partitionsize samples per partition is used.

n_components

number of components to extract. If NA is passed, the same number of components as the input has dimensions is used.

n_components_uwedge

number of components to extract during uwedge approximate joint diagonalization of the matrices. If NA is passed, the same number of components as the input has dimensions is used.

rank_components

boolean, optional. When TRUE, the components will be ordered in decreasing stability.

pairing

either 'complement' or 'allpairs'. If 'allpairs' the difference matrices are computed for all pairs of partition covariance matrices, while if 'complement' a one-vs-complement scheme is used.

groupsize

int, optional. Approximate number of samples in each group when using a rigid grid as groups. If NA is passed, all samples will be in one group unless group_index is passed during fitting in which case the provided group index is used (the latter is the advised and preferred way).

partitionsize

int, optional. Approxiate number of samples in each partition when using a rigid grid as partition. If NA is passed, a (hopefully sane) default is used, again, unless partition_index is passed during fitting in which case the provided partition index is used.

max_iter

int, optional. Maximum number of iterations for the uwedge approximate joint diagonalisation during fitting.

tol

float, optional. Tolerance for terminating the uwedge approximate joint diagonalisation during fitting.

silent

boolean whether to supress status outputs.

Details

For further details see the references.

Value

object of class 'GroupICA' consisting of the following elements

V

the unmixing matrix.

coverged

boolean indicating whether the approximate joint diagonalisation converged due to tol.

n_iter

number of iterations of the approximate joint diagonalisation.

meanoffdiag

mean absolute value of the off-diagonal values of the to be jointly diagonalised matrices, i.e., a proxy of the approximate joint diagonalisation objective function.

Author(s)

Niklas Pfister and Sebastian Weichwald

References

Pfister, N., S. Weichwald, P. Bühlmann and B. Schölkopf (2017). GroupICA: Independent Component Analysis for grouped data. ArXiv e-prints (arXiv:1806.01094).

Project website (https://sweichwald.de/groupICA/)

See Also

The function uwedge allows to perform to perform an approximate joint matrix diagonalization.

Examples

## Example
set.seed(1)

# Generate data from a block-wise variance model
d <- 2
m <- 10
n <- 5000
group_index <- rep(c(1,2), each=n)
partition_index <- rep(rep(1:m, each=n/m), 2)
S <- matrix(NA, 2*n, d)
H <- matrix(NA, 2*n, d)
for(i in unique(group_index)){
  varH <- abs(rnorm(d))/4
  H[group_index==i, ] <- matrix(rnorm(d*n)*rep(varH, each=n), n, d)
  for(j in unique(partition_index[group_index==i])){
    varS <- abs(rnorm(d))
    index <- partition_index==j & group_index==i
    S[index,] <- matrix(rnorm(d*n/m)*rep(varS, each=n/m),
                                                     n/m, d)
  }
}
A <- matrix(rnorm(d^2), d, d)
A <- A%*%t(A)
X <- t(A%*%t(S+H))

# Apply groupICA
res <- groupICA(X, group_index, partition_index, rank_components=TRUE)

# Compare results
par(mfrow=c(2,2))
plot((S+H)[,1], type="l", main="true source 1", ylab="S+H")
plot(res$Shat[,1], type="l", main="estimated source 1", ylab="Shat")
plot((S+H)[,2], type="l", main="true source 2", ylab="S+H")
plot(res$Shat[,2], type="l", main="estimated source 2", ylab="Shat")
cor(res$Shat, S+H)

uwedge

Description

Performs an approximate joint matrix diagonalization on a list of matrices. More precisely, for a list of matrices Rx the algorithm finds a matrix V such that for all i V Rx[i] t(V) is approximately diagonal.

Usage

uwedge(Rx, init = NA, rm_x0 = TRUE, return_diag = FALSE, tol = 1e-10,
  max_iter = 1000, n_components = NA, silent = TRUE)

Arguments

Rx

list of matrices to be diagaonlized.

init

matrix used in first step of initialization. If NA a default based on PCA is used

rm_x0

boolean whether to also diagonalize first matrix in Rx or only use it for scaling.

return_diag

boolean. Specifies whether to return the list of diagonalized matrices.

tol

float, optional. Tolerance for terminating the iteration.

max_iter

int, optional. Maximum number of iterations.

n_components

number of components to extract. If NA is passed, all components are used.

silent

boolean whether to supress status outputs.

Details

For further details see the references.

Value

object of class 'uwedge' consisting of the following elements

V

joint diagonalizing matrix.

Rxdiag

list of diagonalized matrices.

converged

boolean specifying whether the algorithm converged for the given tol.

iterations

number of iterations of the approximate joint diagonalisation.

meanoffdiag

mean absolute value of the off-diagonal values of the to be jointly diagonalised matrices, i.e., a proxy of the approximate joint diagonalisation objective function.

Author(s)

Niklas Pfister and Sebastian Weichwald

References

Pfister, N., S. Weichwald, P. Bühlmann and B. Schölkopf (2017). GroupICA: Independent Component Analysis for grouped data. ArXiv e-prints (arXiv:1806.01094).

Tichavsky, P. and Yeredor, A. (2009). Fast Approximate Joint Diagonalization Incorporating Weight Matrices. IEEE Transactions on Signal Processing.

See Also

The function groupICA uses uwedge.

Examples

## Example
set.seed(1)

# Generate data 20 matrix that can be jointly diagonalized
d <- 10
A <- matrix(rnorm(d*d), d, d)
A <- A%*%t(A)
Rx <- lapply(1:20, function(x) A %*% diag(rnorm(d)) %*% t(A))

# Perform approximate joint diagonalization
ptm <- proc.time()
res <- uwedge(Rx,
              rm_x0=FALSE,
              return_diag=TRUE,
              max_iter=1000)
print(proc.time()-ptm)

# Average value of offdiagonal elements:
print(res$meanoffdiag)