Independent Component Analysis

We apply the Independent Component Analysis to find underlying independent sources from observed mixtures of signals. There are certain assumptions underlying this method:

• the statistical independence of the source signals
• the observed signals being a linear combination of the source signals
• the sources of the signals are non-Gaussian

Fitting the Model

The source signals used here are three sinusoids:

• Source 1: $\sin(2\pi t)$
• Source 2: $\sin(12\pi t)$
• Source 3: $\sin(26\pi t)$

The observed signals are as follows:

• Observation 1: $\sin(2\pi t) + \sin(12\pi t) + \sin(26\pi t)$
• Observation 2: $0.5\sin(2\pi t) + 2\sin(12\pi t) + \sin(26\pi t)$
• Observation 3: $1.5\sin(2\pi t) + \sin(12\pi t) + 2\sin(26\pi t)$

Source ⇨ Observed

CODE

long seed = 32; //For random state initialisation weights
ICA obj = new ICA(observed, seed); //observed is double[][]
obj.fit();
double[][] recovered = obj.transform();

Observed ⇨ Recovered

Recovering from fitted ICA

CODE

double[][] recovered_unknown = obj.transform(unknown); //unknown is double[][]

Unknown Observed ⇨ Recovered