Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources

Abstract

An extension of the infomax algorithm of Bell and Sejnowski (1995) ispresented that is able blindly to separate mixed signals with sub-and supergaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have sub-and supergaussian regimes were used to derive a general learning rule that preserves the simple architecture proposed by Bell and Sejnowski (1995), is optimized using the natural gradient by Amari (1998), and uses the stability analysis of Cardoso and Laheld (1996) to switch between sub-and supergaussian regimes. We demonstrate that the extended infomax algorithm is able to separate 20 sources with a variety of source distributions easily. Applied to high-dimensional data from electroencephalographic recordings, it is effective at separating artifacts such as eye blinks and line noise from weaker electrical signals that arise from sources in the brain.

A method for multitask fMRI data fusion applied to schizophrenia

“…To mitigate this concern in this initial jICA approach, we normalize the AOD and SB data and utilize the extended infomax algorithm that adaptively models the sources as having either supergaussian (e.g., a distribution with positive kurtosis) or subgaussian distribution. This algorithm has shown to be quite robust to violations of the underlying model for a wide variety of data types [Lee et al, 1999] and enables some flexibility in the source distributions. This is confirmed in our own data because upon examination of the distributions of the joint sources, we find that the distribution of the AOD and SB parts of the same source do show some variation (they have different means, variances, etc.…”

“…6. Spatial ICA decomposition: The extended-infomax algorithm [Bell and Sejnowski, 1995;Lee et al, 1999] was used to decompose the reduced feature matrix to maximally independent component images and subjectspecific mixing (loading) parameters. 7.…”

Unmixing concurrent EEG-fMRI with parallel independent component analysis

“…We see a major utility for parallel ICA in this context as it provides the means to disentangle and visualize these networks both in their spatial and temporal form (Calhoun, et al, 2006a;Debener, et al, 2006;Makeig, et al, 2004a;McKeown, et al, 2003;Onton, et al, 2006). However, some limitations apply: Infomax assumes sources to have non-normal, either superor subgaussian distributions (Bell, et al, 1995;Lee, et al, 1999), and this seems to hold for a great variety of physiological signals as well as technical artefacts. However, if sources (or noise) are gaussian, ICA will split these up into spurious non-gaussian components.…”

“…Following the above arguments, we develop an analysis framework for group data that employs Infomax independent component analysis (ICA, Bell, et al, 1995;Lee, et al, 1999; for an overview see Stone, 2002) to recover a set of statistically independent maps from the fMRI (sICA), and independent time-courses from the EEG (tICA) separately, and match these components across modalities by correlating their trial-to-trial modulation. ICA was developed to address linear mixing problems similar to the 'cocktail party problem' in which many people are speaking at once and multiple microphones pick up different mixtures of the speakers' voices (Bell, et al, 1995).…”

Joint independent component analysis for simultaneous EEG–fMRI: Principle and simulation

“…If one additionally assumes joint independence of the fMRI and EEG portions of the sources, respectively, one can use e.g. extended Infomax ICA which employs a gradient ascent algorithm to maximize the entropy of the output of a single layer neural network (Bell, et al, 1995;Lee, et al, 1999).…”