Introduction - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 17

empowered by suitable software for classifying the status of marble block-shaped
materials building a low-cost operating system. This system might be valuable to
improve the cutting of the blocks. In the second prototype, the standardization of
an efficient and non-destructive method for ceramic characterization based on
ultrasonic testing will be an important contribution for archaeologists. The
developed prototype demonstrated that it could complement or replace destructive,
costly, and time-consuming techniques, which are currently being used by
archaeologists in the area of ceramic characterization. The techniques for char-
acterization and dating of archaeological ceramics that include thermolumines-
cence, chemical methods, and thin section microscopy [ 62 ] are destructive, slow,
and expensive.

1.3 Contributions

The thesis makes a number of contributions to the research in ICA. The funda-
mental contribution is a general framework for ICA mixture modelling. Further
contributions are: a hierarchical method to obtain higher-level structures of clas-
sification from ICA mixture parameters; the introduction of sequential depen-
dences in the classification of ICA mixtures; and the introduction of ICA and ICA
mixtures in diverse novel applications. These applications are: material quality
control using impact-echo testing, chronological cataloguing of archaeological
ceramics, diagnosis of the restoration in historical buildings, diagnosis of sleep
disorders, and discovery of student learning styles in web-log data.

1.3.1 ICA Mixture Modelling

A procedure is proposed that introduces the following new aspects in ICAMM: (i)
Non-parametric estimation of the source pdf; (ii) Estimation of residual depen-
dencies after ICA, and the consequent correction of the probabilities of every class
to the observation vector; (iii) Supervised-unsupervised learning of the model
parameters; and (iv) Incorporation of any ICA algorithm into the learning of the
ICA mixture model. The final procedure was called ''Mixca'' (Mixture of Com-
ponent Analyzers) since the independence assumption of ICA is relaxed by the
proposed posterior probability correction [ 63 ].
It is assumed that every class satisfies an ICA model: vectors x k corresponding
to a given class C k k ¼ 1 ; ... ; K are the result of applying a linear transformation
A k to a (source) vector s k ; whose elements are independent random variables, plus
a bias or centroid vector b k ; i.e., x k ¼ A k s k þ b k k ¼ 1 ; ... ; K : Thus, Mixca is a
non-linear mixture processor that fits the structure shown in Fig. 1.7 . This structure
has K processing channels, which are linear processors that implement the ICA
equation s k ¼ A 1
k

ð x b k Þ followed by a non-linear processor g ð s k Þ: