Introduction - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 14

Fig. 1.6 A dynamic model (observation vector x t and hidden state vector y t )

Hierarchical clustering algorithms have been used in a large potpourri of
applications, for instance, image segmentation, object and character recognition,
documental retrieval, data mining, and biomedical applications. These applica-
tions include: raster, texture, and multispectral medical image segmentation
[ 39 ]; topic extraction from text corpus [ 42 ]; word sense disambiguation [ 43 ];
on-line mining of web sites usage and automatic construction of portal sites
[ 44 ]; extracting financial data for business valuation [ 45 ]; grouping of
non-stationary time series of industrial production indices [ 46 ]; gene expression
(gene versus time, gene versus tissue, gene versus patient), interactomes
(protein-protein interaction networks) and sequences (clustering protein fami-
lies) [ 47 ]. A review of applications in engineering of clustering techniques can
be found in [ 48 ].

1.1.4 Non-Linear Dynamic Modelling

The procedures developed in the thesis are principally focused on the analysis of
ICA mixtures from static models. However, in Chap. 7 we present a procedure to
extend ICAMM to the case of having sequential dependence in the feature
observation record that we have called sequential ICAMM (SICAMM). We use
this basis to introduce the analysis of ICA mixtures in dynamic models. Since
SICAMM is defined from the classical Hidden Markov Model (HMM), the main
definitions of HMM are reviewed in this section.
The basic assumption in dynamic modelling is that there exist hidden states
(a hidden stochastic process) corresponding to a nonstationary model. The model
can be defined using HMM having discrete states, or Kalman filters having con-
tinuous states. Figure 1.6 shows a general dynamic model with observation x t and
unobserved hidden state y t . The system is characterized by a state transition
probability P ð y t þ 1 j y t Þ and a state to observation probability P ð x t j y t Þ .
The method for predicting future events under such a dynamic model is to
maintain a posterior distribution over the hidden state y t þ 1 based on all