Simple, Robust, and Memory-Efficient FastICA Algorithms Using the Huber M-Estimator Cost Function

Authors: Douglas, Scott; Chao, Jih-Cheng

Source: The Journal of VLSI Signal Processing, Volume 48, Numbers 1-2, August 2007 , pp. 143-159(17)

Publisher: Springer

Abstract:

The goal of blind source separation is to separate multiple signals from linear mixtures without extensive knowledge about the statistical properties of the unknown signals. The design of separation criteria that achieve accurate and robust source estimates within a simple adaptive algorithm is an important part of this task. The purpose of this paper is threefold: (1) We introduce the Huber M-estimator cost function as a contrast function for use within prewhitened blind source separation algorithms such as the well-known and popular FastICA algorithm of Hyvärinen and Oja. The resulting algorithm obtained from this cost is particularly simple to implement. We establish key properties regarding the local stability of the algorithm for general non-Gaussian source distributions, and its separating capabilities are shown through analysis to be largely insensitive to the cost function's single threshold parameter. (2) We illustrate the use of the Huber M-estimator cost as a criterion within the winning algorithm entry for the blind source separation portion of the first Machine Learning for Signal Processing Workshop Data Analysis Competition, describing the key features of the algorithm design for successful separation of large-scale and ill-conditioned signal mixtures with reduced data set requirements. (3) We show how the FastICA algorithm can be implemented without significant additional memory resources by careful use of sequential processing strategies.

Keywords: Huber M-estimator; FastICA algorithm; ill-conditioned signal mixtures; kurtosis-based contrasts; Gaussian noise; non-Gaussian source distributions

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11265-007-0046-9

Affiliations: 1: Email: douglas@engr.smu.edu

Publication date: 2007-08-01

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