Generalized Component Analysis and Blind Source Separation Methods for Analyzing Multichannel Brain Signals

Blind source separation (BSS) and related methods, e.g., independent component analysis (ICA) are generally based on a wide class of unsupervised learning algorithms and they found potential applications in many areas from engineering to neuroscience. The recent trends in blind source separation and generalized component analysis (GCA) is to consider problems in the framework of matrix factorization or more general signals decomposition with probabilistic generative models and exploit a priori knowledge about true nature, morphology or structure of latent (hidden) variables or sources such as sparseness, spatio-temporal decorrelation, statistical independence, nonnegativity, smoothness or lowest possible complexity. The goal of BSS can be considered as estimation of true physical sources and parameters of a mixing system, while objective of GCA is finding a new reduced or hierarchical and structured representation for the observed (sensor) data that can be interpreted as physically meaningful coding or blind signal decompositions. The key issue is to find a such transformation or coding which has true physical meaning and interpretation. In this paper we discuss some promising applications of BSS/GCA for analyzing multi-modal, multi-sensory data, especially EEG/MEG data. Moreover, we propose to apply these techniques for early detection of Alzheimer disease (AD) using EEG recordings. Furthermore, we briefly review some efficient unsupervised learning algorithms for linear blind source separation, blind source extraction and generalized component analysis using various criteria, constraints and assumptions. A fairly general blind signal separation (BSS) problem often referred as blind signal decomposition or blind source extraction (BSE) can be formulated as follows (see Figure 1). We observe records of sensor signals x(t) = [x1(t), . . . , xm(t)] , where t is time and (·)T means transpose of a vector, from a MIMO (multiple-input/multiple-output) dynamical (mixing and filtering) system. These signals are usually superposition of unknown source signals and noises. The objective is to find an inverse system, sometimes termed a reconstruction system, neural network or a inverse system, if it exists and is stable, in order to estimate the all primary source signals s(t) = [s1(t), . . . , sn(t)] or only some of them with