Introduction - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 23

source pdf's, semi-supervised learning, use of any ICA algorithm in the parameter
updating, and a correction of the posterior probability after convergence. After-
ward, this chapter explores the performance of the algorithm by an extensive set of
simulations and experiments. The simulations include: performance in BSS,
classification of ICA mixtures, classification of ICA mixtures with nonlinear
dependencies, and semi-supervised learning. The results are discussed and com-
pared with several standard ICA algorithms.
Chapter 4 describes a postprocessing method to be applied after obtaining the
parameters of the ICA mixtures by a non-parametric method as the one described
in Chap. 3 . The method consists of a hierarchy algorithm that composes an
agglomerative (bottom-up) clustering from the estimated parameters (basis vectors
and bias terms) of the ICA mixture. The merging at different levels of the hier-
archy is performed using the Kullback-Leibler distance between clusters. The
method is validated from several simulations (including ICA mixtures with uni-
form and Laplacian source distributions) and from processing real data. The
applications are image processing segmentation and clustering, and classification
of materials tested using impact-echo. Meaningful hierarchical levels are dem-
onstrated for the experiments from the ICA mixture parameters to higher-level
structures. The hierarchical levels for image processing represent concepts of
similarity in a set of images of different objects or in patches of an image.
Novel applications of the algorithmic methods developed in Chaps. 3 and 4 are
covered in the following chapters. Chapters 5 and 6 are devoted to NDT appli-
cations, and Chap. 7 is dedicated to biosignal processing and webmining.
Chapter 5 presents a model for the classification of materials evaluated by the
impact-echo testing technique. It is demonstrated that several kinds of defects are
characterized by the parameters of different ICA models from the mass spectra of
the impact-echo test. This modelling, allows the following levels of classifications:
(i) Material condition homogeneous, one defect, multiple defects; (ii) Kind of
defect homogeneous, hole, crack, multiple defects; (iii) Defect orientation
homogeneous, hole in the X axis or Y axis, crack in the XY, ZY, or XZ planes,
multiple defects; and (iv) Defect dimension homogeneous, passing through or half-
passing through holes and cracks of classification level (iii), multiple defects. The
chapter includes results from a large number of lab experiments. The performance
of the classification by ICA mixtures using Mixca is compared with linear dis-
criminant analysis (LDA) and with multi-layer perceptron (MLP) classification.
Chapter 6 includes two applications in the NDT field. The first application
comprises the classification of several archaeological ceramic shards from dif-
ferent deposits in the eastern part of Spain. The pieces are measured by ultrasounds
using an ad hoc device. The features extracted from the ultrasonic signals are
classified using the following algorithms: LDA, MLP, RBF, learning vector
quantization (LVQ), k-nearest neighbours (kNN), and Mixca. The classification
performed was chronological period: the Bronze Age, Iberian, Roman, and the
Middle Ages. The best performance in classification is obtained for different ratios
of semi-supervised training of Mixca. Some of the pieces were characterized using
physical

and chemical analyses. A rationale of the results that shows the