Implementation:Haifengl Smile ICA

Knowledge Sources	Haifengl_Smile
Domains	Signal Processing, Dimensionality Reduction, Machine Learning
Last Updated	2026-02-08 22:00 GMT

Overview

ICA is a record class implementing Independent Component Analysis using the FastICA algorithm to separate a multivariate signal into additive, statistically independent components.

Description

ICA implements the FastICA algorithm by Aapo Hyvarinen for Independent Component Analysis. The algorithm seeks an orthogonal rotation of prewhitened data through a fixed-point iteration scheme that maximizes a measure of non-Gaussianity of the rotated components. Non-Gaussianity serves as a proxy for statistical independence.

The class supports three built-in contrast (non-linear) functions:

• LogCosh - based on the log of the hyperbolic cosine function.
• Gaussian (Exp) - based on the exponential function.
• Kurtosis - based on the fourth-order cumulant.

The algorithm performs data centering and whitening (via eigenvalue decomposition of the covariance matrix) before applying the fixed-point iterations. Each independent component is orthogonalized against previously found components using deflation.

The nested Options record encapsulates hyperparameters (contrast function, max iterations, tolerance) and supports serialization to/from Properties.

Usage

Use ICA for blind source separation problems such as the cocktail party problem, artifact removal in EEG/MEG signals, feature extraction, or any scenario where you need to decompose observed mixed signals into independent source signals. At least N observations are needed to recover N independent sources.

Code Reference

Source Location

• Repository: Haifengl_Smile
• File: base/src/main/java/smile/ica/ICA.java
• Lines: 1-310

Signature

public record ICA(double[][] components) implements Serializable {
    // Nested Options record
    public record Options(DifferentiableFunction contrast, int maxIter, double tol) {
        public Options(DifferentiableFunction contrast, int maxIter);
        public Options(String contrast, int maxIter);
        public Properties toProperties();
        public static Options of(Properties props) throws ReflectiveOperationException;
    }

    // Fitting methods
    public static ICA fit(double[][] data, int p);
    public static ICA fit(double[][] data, int p, Options options);
}

Import

import smile.ica.ICA;

I/O Contract

Inputs

Name	Type	Required	Description
data	double[][]	Yes	Training data matrix. Rows correspond to source signals (observations), columns correspond to samples.
p	int	Yes	The number of independent components to extract (1 <= p <= number of rows in data).
options	ICA.Options	No	Hyperparameters: contrast function (default LogCosh), maxIter (default 100), tolerance (default 1E-4).

Outputs

Name	Type	Description
ICA	ICA	The fitted ICA model.
components()	double[][]	The independent components. Each row is an independent component vector.

Usage Examples

Basic Usage

import smile.ica.ICA;

// Mixed signals: rows are observations, columns are time samples
double[][] mixedSignals = new double[3][1000];
// ... populate with mixed signal data ...

// Fit ICA with 3 independent components using default LogCosh contrast
ICA ica = ICA.fit(mixedSignals, 3);

// Access the separated components
double[][] components = ica.components();
// components[0], components[1], components[2] are the independent sources

With Custom Options

import smile.ica.ICA;

// Configure with Gaussian contrast function, 200 iterations, tolerance 1E-5
ICA.Options options = new ICA.Options("Gaussian", 200);

double[][] data = new double[4][5000];
// ... populate data ...

ICA ica = ICA.fit(data, 2, options);
double[][] components = ica.components();

Persistence with Properties

import smile.ica.ICA;
import java.util.Properties;

// Save options to properties
ICA.Options options = new ICA.Options("LogCosh", 100);
Properties props = options.toProperties();

// Restore options from properties
ICA.Options restored = ICA.Options.of(props);