Introduction - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 2

recognition as a search for structure in data [ 2 ]. The principal task of pattern
recognition that we are interested in is in dividing a manifold of data into cate-
gories that have a meaning under an application context. We will approach this
task from two perspectives: classification and clustering. The first one considers a
predefined set of categories to which data items can be assigned; the second one
discovers significant groups that are present in a data set with no predefined classes
and no examples that would show what kind of desirable relations should be valid
among the data. The structures searched for in the data consist of the rules that
describe the relationships in the data. These structures can be defined through a
probabilistic model that can provide a reasonable explanation of the process
generating the data. We assume that the set of observed variables that are
explicitly defined in the data are generated from a set of hidden variables of an
underlying model. Thus, the data are denoted by formulae or models that describe
their principal characteristics. The ratio of the complexity of the data set to the
complexity of the formulae is defined as parsimony. In order to propose a model
for the data, it is necessarily assumed that there exist patterns or rules in the data.
In this case, the data are redundant, and the patterns may be used to provide a
parsimonious description that is more concise than the data themselves [ 3 ].
Pattern recognition is frequently achieved by using features extracted from the
raw data either because the stream of the measured data is large or because
processing raw data does not allow patterns to be distinguished. Thus, the selection
and estimation of the features should lead to adequately characterizing the con-
spicuous properties of the data. An appropriate set of features allows the data to be
separated in different groups or clusters, where the data in one group are the most
similar to each other, and are also the most dissimilar to the data in others groups.
The groups of data extracted from the original data manifold represent particular
patterns with particular meanings for which an explicit label could be assigned.
Once the rules for the patterns are learned from a dataset, they can be applied to
classify new datasets.
There can be different degrees of completeness of the knowledge of the labels for
the dataset employed in the learning process. The degree of knowledge available
determines the kind of learning, i.e., supervised (all the data-label pairs are known),
semi-supervised (labels are available for a subset of the data), and unsupervised (no
labels are available). The kind of learning must be encompassed within the com-
plexity of the real-world problem that imposes a minimum level of labelling in
order to learn the geometry of the data. Increasing the data labels available in order
to reach an adequate level is restricted for several applications. Frequently,
obtaining unlabelled data may be relatively easy whereas obtaining labelled data
may be difficult and costly. However, the latter can be alleviated by considering that
the performance of some algorithms is significantly improved with a small number
of labelled data [ 4 , 5 ]. Therefore, semi-supervised learning has been increasingly
studied (for its capability to incorporate different proportions of unlabelled and
labelled data) as a suitable method for many complex problems [ 6 ].
Intelligent signal processing algorithms provide an important tool to support
automatic

pattern recognition, to gain insight into problem-solving, and to