Conclusions - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 172

simple models offers greater ease of interpretation (different levels of generalization
and abstraction) as well as the benefits of analytical and computational simplification.
The application of the method was demonstrated for several simulations (compared
with the single-linkage method) and the analyses of real images. In the simulations,
the results showed that the binary trees obtained by the proposed method perform
better than the single-linkage method to capture hierarchical data organization. Real
data analysis showed meaningful dendrograms obtained for classification of images
of objects with similar shapes, and segmentation of natural images.
The proposed methods build a versatile and powerful framework that can be
employed in many real-world problems involving complex data densities. In
Chaps. 5 , 6 , and 7 , we provided several applications in signal classification and
pattern recognition that processed different kinds of data: sonic and ultrasonic
signals; EEG signals; images; and historic web log data. These chapters also
included the following theoretical contributions: a method to introduce sequential
dependencies in ICAMM-based classification (that was applied to sleep disorders
analysis); and different approaches to establish the relation between the underlying
physical model of the application and the probabilistic model ICA or ICAMM.
Besides the image processing analyses of Chap. 4 , the application chapters dealt
with the following challenging problems: diagnosis of the restoration of a his-
torical building; classification of the chronological period of archaeological
ceramics; classification of up to 12 kinds of different defective materials using
impact-echo testing; detection of micro arousals in apnea patients; and detection of
learning styles for the students in a virtual university (webmining). The ICAMM
parameters enable a detailed explanation of the measured signals and their source
data generators. In any case, even though the complexity of the problem constrains
a physical interpretation, the framework can be used as a general data mining
technique as demonstrated in the webmining application. The degrees of freedom
afforded by the proposed methods allow the adaptation to and the solving of a
broad range of real-world problems.
8.2 Contribution to Knowledge
This section lists the contributions that this thesis makes to the field of ICA and
ICAMM. The thesis contributions are the following:
• A novel procedure for learning mixtures of independent component analyzers
has been proposed ( Sect. 3.3 ), which we call Mixca. The algorithm estimates
the ICAMM parameters through the maximization of a single likelihood
function. The technique of optimization applied was natural gradient, which
simplifies the learning rule and speeds convergence. Four new extensions
towards generalization of the ICAMM method were formulated: (i) incor-
poration of any kind of learning (unsupervised, semi-supervised, supervised);
(ii) non-parametric kernel-based estimation of source densities; (iii) support