On statistical pattern recognition in independent component analysis mixture modelling
- Autores: Addisson Salazar Afanador
- Directores de la Tesis: Luis Vergara Domínguez (dir. tes.), Jorge Igual García (codir. tes.)
- Lectura: En la Universitat Politècnica de València ( España ) en 2011
- Idioma: español
- Tribunal Calificador de la Tesis: Alberto González Salvador (presid.), Jorge Gosálbez Castillo (secret.), Christian Jutten (voc.), Juan Ramón Vidal Romaní (voc.), Miguel Angel Lagunas Hernández (voc.)
- Materias:
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- Resumen
The framework of this thesis is in the field of statistical pattern recognition from data modelling based on mixtures of non-gaussian distributions. The fundamental area of this research work is independent component analysis (ICA), whose principal hypothesis considers that observed signals are linear transformations of data generated from a set of hidden variables (termed sources or components). ICA techniques allow the extraction of such components reducing the higher-order statistical dependencies among them. Thus, the original M-dimensional probability density function (pdf) of the data is factored in the component space as the product of one-dimensional probability densities. This becomes a great simplification from the point of view of data probabilistic modelling. The thesis is based on a generalized ICA model in which multiple ICA structures are considered in order to achieve versatile pdf modelling. This approach is known as independent component analysis mixture modelling (ICAMM). The problems dealt with here are signal classification and blind source separation (BSS).
This thesis makes a number of contributions to ICA and ICAMM research: (i) a versatile method for ICAMM that includes: semi-supervised learning, non-parametric estimation of the source densities, estimation of residual dependencies for correction of posterior probabilities, and incorporation of any ICA algorithm into the learning of the ICAMM parameters; (ii) a hierarchical clustering method to derive higher level structures of classification from the ICAMM parameters; (iii) a method to introduce sequential dependencies in classification of ICA mixtures; and (iv) introduction of ICA and ICAMM in diverse novel applications, attempting as much as possible to establish a relation between the underlying physical model and the probabilistic model by ICAMM.
The developed methods were validated by means of an extensive number of simulations in different scenarios by varying the following parameters: degrees of linearity in the data; kinds of source distributions; unsupervised, semi-supervised, and supervised learning; and different numbers of clusters. Several figures of merit were defined in order to test the performance of the proposed methods in comparison with classical BSS-ICA and classification techniques. In addition to the simulated signals, real data of different types were processed including sonic, ultrasonic, and electroencephalographic signals; images; and historical data from a virtual campus web.
The applications explored in the thesis are the following: material quality control using the impact-echo technique; chronological cataloguing of archaeological ceramics; diagnosis of historic building restoration; diagnosis of sleep disorders; and the discovery of learning styles in e-learning. The developed methods were also employed in classic applications of image processing such as object recognition and image segmentation. The results demonstrate the capability and flexibility of the proposed methods to be adapted to different problems in order to find significant structures in data. These structures were detected in the ICAMM parameters (mixture matrices, source vectors, and cluster centroids).
