Introduction - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 3

complement expert decision-making 0 [ 7 - 9 ]. These algorithms usually make
assumptions about the data-generating process, for instance, modelling the data as
a mixture of data generators or analyzers considering that each generator produces
a particular group of data. The independent component analysis mixture modelling
(ICAMM) [ 10 , 11 ] has recently emerged as a flexible approach to model arbitrary
data densities using mixtures of multiple independent component analysis (ICA)
models [ 12 - 14 ] with non-gaussian distributions for the independent components
(i.e., relaxing the restriction of modelling every component by a multivariate
Gaussian probability density function). ICA is an intensive area of research that is
progressively finding more applications for both blind source separation (BSS) and
for feature extraction/modelling. The goal of ICA is to perform a linear trans-
formation of the observed sensor signals, such that the resulting transformed
signals (the sources or prior generators of the observed data) are as statistically
independent of each other as possible. In comparison to correlation-based trans-
formations such as principal component analysis (PCA), ICA not only decorrelates
the sensor observations composed of mixed signals (in terms of second-order
statistics), but it also reduces the higher-order statistical dependencies among them
[ 13 - 18 ].
Applications of ICA comprise such diverse disciplines as: speech separation;
biomedical applications (removing electrocardiogram (ECG) and electroenceph-
alogram (EEG) artefacts, noninvasive fetal ECG extraction, separation and
determination of brain activity sources, diagnosis of atrial fibrillation, extraction of
sources of neural activity in the brain) [ 19 - 23 ]; image processing (recognition of
faces using ICA bases, spatial edge filters using separating matrix, reconstruction
and restoration of distorted images); text classification; non-destructive testing
(NDT) (analysis of the vibration in mechanical systems: termite activity in wood,
identification of transient low-events in diesel engines, identification of particular
faults for gearbox diagnostics); and telecommunications (remove interfering
transmission in wireless telecommunications systems, blind code-division multiple
access) [ 13 - 18 ].
The linear ICA method is extended in ICAMM to a kind of nonlinear ICA
model, i.e., multiple ICA models are learned and weighted in a probabilistic
manner. Thus, the ICA mixture model is a conditional independence model, i.e.,
the independence assumption holds only within each class and there may be
dependencies among the classes [ 10 ]. The degrees of freedom afforded by mixtures
of ICAs allow a broad range of real problems involving complex data densities to
be dealt with. ICAMM contributes to obtaining higher insights into the applica-
tions since this modelling performs both source extraction and signal analysis
simultaneously. This enables a more detailed explanation of the measured signals
and of the source data generators that are behind the observed mixture. The
suitability of mixtures of ICA for a given problem of data analysis and classifi-
cation can be treated from different perspectives. First, there is the ''least physical''
interpretation, which assumes that ICA mixture learning underlies estimation/
modelling of the probability density of multivariate data [ 11 ]. Second, there is the
interpretation of ICA as a way of learning some bases (usually called activation