clusterICA: Independent Component Analysis (ICA)

In pws3141/clusterICA: Approximate Independent Component Anaylsis

Description

Uses random directions, clustering and optimisation to obtain ICA loadings, using the m-spacing entropy estimation as the objective function to minimise.

Usage

clusterICA(X, p.ica = -1, p.whiten = -1, rand.iter = -1, m = -1,
  kmean.tol = 0.1, opt.maxit = 5000, opt.method = "BFGS",
  fast.init = NA, compute.scores = TRUE, verbose = FALSE)

Arguments

X	the data to perform ICA on, ncol(x) = n, nrow(x) = p
p.ica	the number of ICA loadings outputted
p.whiten	(optional) the size of the whitened matrix, i.e. how many PCA loadings to keep in the whitening step
rand.iter	the number of random directions to initialise
m	(optional) the value of m-spacing for calculating approximate entropy, if missing(m), m <- sqrt(n)
kmean.tol	the tolerance used in divisive clustering, see clusterProjDivisive
opt.maxit	the maximum number of iterations used in the optimisation step, see optim
opt.method	the method used in the optimisation step, see optim
fast.init	if TRUE then the objective function used in the fastICA method is optimised to find an extra direction to cluster
compute.scores	if TRUE then scores of the whitened data are outputted
verbose	if TRUE then information is given on the status of the function

Value

An object of class ‘coords’, with the following additional components added:

• X Centered data matrix

• Y Whitened data matrix, found using jvcoords::whiten(x)

• S Matrix of source signal estimates

• W Estimated unmixing matrix, S = X t(W)

• R Orthogonal rotation matrix, S = Y R

• entr The m-spacing entropy of each column of S

Author(s)

Paul Smith, [e-mail]

Examples

#---------------------------------------------------
#Example 1: un-mixing two stratified independent normals
#---------------------------------------------------
p <- 2
n <- 10000
set.seed(1243)
x1 <- matrix(rnorm(n*p, mean = 2.5), n, p)
x1[,2] <- scale(x1[,2])
a1 <- c(0.2,1)
a1 <- a1 / sqrt(sum(a1^2))
good1 <- cos(20 * x1 %*% a1) >= 0
x1Good <- x1[which(good1),]
x2 <- matrix(rnorm(n*p, mean = -2.5), n , p)
x2[,2] <- scale(x2[,2])
good2 <- cos(20 * x2 %*% a1) >= 0
x2Good <- x2[which(good2),]
xGood <- rbind(x1Good, x2Good)
a <- clusterICA(X=xGood, p.ica=1, rand.iter=1000)
par(mfrow = c(1,3))
plot(xGood, main = "Pre-processed data")
plot(a$Y, main = "Whitened data")
plot(density(a$S, bw="sj"), main = "ICA components")

#---------------------------------------------------
#Example 2: un-mixing two mixed independent uniforms
#From fastICA man page
#---------------------------------------------------
S <- matrix(runif(10000), 5000, 2)
A <- matrix(c(1, 1, -1, 3), 2, 2, byrow = TRUE)
X <- S %*% A
a <- clusterICA(X, p.whiten=2, rand.iter=1000)
par(mfrow = c(1, 3))
plot(X, main = "Pre-processed data")
plot(a$Y, main = "Whitened data")
plot(a$S, main = "ICA components")

#---------------------------------------------------
#Example 3: un-mixing iris data
#---------------------------------------------------
a <- clusterICA(iris[,1:4])
plot(a$S, main = "ICA components")
pairs(a$S, col=iris$Species)

pws3141/clusterICA documentation built on July 14, 2020, 5:04 a.m.