ICA

This is an example for ICA(Independent Component Analysis) with R program.

We will use the function from “fastICA” package to achieve our goal.

1. Create Source matrix(S) and Mixing matrix(A):

library(fastICA)

# Source matrix
S <- cbind(sin((1:1000)/20), rep((((1:200)-100)/100), 5))
# Mixing matrix
A <- matrix(c(0.291, 0.6557, -0.5439, 0.5572), 2, 2)
# plot graphs
par(mfcol = c(1, 2))
plot(1:1000, S[,1], type = "l",xlab = "S1", ylab = "")
plot(1:1000, S[,2], type = "l", xlab = "S2", ylab = "")

2. Mix two signals with the Mixing Matrix(A):

# Mixed two signals
X <- S %*% A

par(mfcol = c(1, 2))
plot(1:1000, X[,1], type = "l",xlab = "X1", ylab = "")
plot(1:1000, X[,2], type = "l", xlab = "X2", ylab = "")

3. Use ICA algorithm to estimate source signals:

# ICA for extracting independent sources from mixed signals
a <- fastICA(X, 2, alg.typ = "parallel", fun = "logcosh", alpha = 1,
             method = "R", row.norm = FALSE, maxit = 200,
             tol = 0.0001, verbose = TRUE)
## Centering
## Whitening
## Symmetric FastICA using logcosh approx. to neg-entropy function
## Iteration 1 tol = 0.1186187
## Iteration 2 tol = 0.002116623
## Iteration 3 tol = 2.003116e-06
par(mfcol = c(1, 2))
plot(1:1000, a$S[,1], type = "l", xlab = "S'1", ylab = "")
plot(1:1000, a$S[,2], type = "l", xlab = "S'2", ylab = "")

‧The combination of 6 graphs above: