Robust Independent Component Analysis for Cognitive Informatics

Introduction

Functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) signals are two standard tools for investigating brain activity and, in turn, human cognition, as studied in cognitive informatics (Zhang, Wang, & Kinsner, 2007) and other disciplines. Of particular interest are the location of various activities within the brain and the dynamics of those functional regions as observed through the EEG signal. While fMRI shows the location of the active brain regions reasonably well, the recorded temporal EEG signal may not be a good indicator of the dynamics because it does not originate from the brain alone, but is a mixture of the EEG itself with the electrocardiogram (ECG) representing heart activity and the electromyogram (EMG) caused by the activity of the muscular system. In addition, the EEG and EMG signals have non-Gaussian probability distribution functions (pdfs) and broadband coloured noise-like frequency spectra. Consequently, to reduce the impact of such unwanted signals, demixing of the recorded EEG signal should be used. A technique called independent component analysis (ICA) can demix the recordings in order to analyze them as close to their pure forms as possible (Gadhok, 2006; Hyvärinen, Karhunen, & Oja, 2001; Makeig et al., 2002; McKeown et al., 1998).

However, various ICA algorithm implementations are sensitive to outliers (i.e., the extreme values that do not comply with the pdf of the signal) because the implementations are based on high-order statistics that include moments higher than two. In fact, contamination of biomedical recordings by outliers is an unavoidable aspect of signal processing. For example, Hampel, Ronchetti, Rousseeuw, and Stahel (1986) provided a real-world situation related to EEG data obtained by a fully automatic recorder. The recorder equipment was working properly and the histogram was adequate except for some seemingly unimportant jitter of the plotter in the tails in the pdf. Yet, the third and fourth moments were far too large. A search revealed that there was a spike of about two dozen out of a quarter million data points when the equipment was turned on, and these few points caused the high moments and the jitter in the plot. Thus, the impact of outliers on the signal separation performance of an ICA algorithm is an important characteristic in assessing the algorithm’s utility for cognitive informatics.

Blind source separation (BSS) is defined as the problem of demixing an additive combination of statistically independent signals based on observations of those mixtures only. ICA is a statistical method for extracting sources from their mixtures without the knowledge of the sources themselves. It uses the information contained in the higher order statistics of the observed mixtures, under the assumption of non-Gaussian distributed sources, to separate the signals into their original sources up to an arbitrary scale and permutation (Hyvärinen et al., 2001).

The objective of this article is to study the outlier sensitivity of ICA algorithms in an unbiased optimization-landscape environment by measuring their separation performance and changes to their respective contrast functions (ICA estimators) in an outlier-contaminated simulation. This is a novel approach as most ICA outlier robustness research has been concerned with either the boundedness of the influence function (IF) of an ICA estimator, or the separation performance in a biased optimization-landscape environment with outlier-contaminated simulations (Hampel et al., 1986; Hyvärinen et al., 2001; Minami & Eguchi, 2003).