A Fast Fixed-Point Algorithm for Independent Component Analysis

TLDR

The paper proposes a novel fast algorithm for independent component analysis applicable to blind source separation and feature extraction. The algorithm transforms a neural‑network learning rule into a parameter‑free fixed‑point iteration that sequentially extracts all non‑Gaussian independent components, operating in batch or semi‑adaptive mode. Convergence is rigorously proved with cubic speed, and experiments show the method is 10–100 times faster than gradient‑based algorithms, often converging in only a few iterations.

Abstract

We introduce a novel fast algorithm for independent component analysis, which can be used for blind source separation and feature extraction. We show how a neural network learning rule can be transformed into a fixedpoint iteration, which provides an algorithm that is very simple, does not depend on any user-defined parameters, and is fast to converge to the most accurate solution allowed by the data. The algorithm finds, one at a time, all nongaussian independent components, regardless of their probability distributions. The computations can be performed in either batch mode or a semiadaptive manner. The convergence of the algorithm is rigorously proved, and the convergence speed is shown to be cubic. Some comparisons to gradient-based algorithms are made, showing that the new algorithm is usually 10 to 100 times faster, sometimes giving the solution in just a few iterations.