Resumen de tesis doctoral

Restricted Conceptual Clustering Algorithms based on Seeds

Algoritmos Conceptuales Restringidos basados en Semillas

Graduated: Irene Olaya Ayaquica Martínez
National Institute of Astrophysics, Optics and Electronics
Luis Enrique Erro # 1, Santa María Tonantzintla, C.P. 72840, Puebla, México.

Advisor: José Francisco Martínez Trinidad
National Institute of Astrophysics, Optics and Electronics
Luis Enrique Erro # 1, Santa María Tonantzintla, C.P. 72840, Puebla, México.
e–mail: fmartine@inaoep.mx

Advisor: Jesús Ariel Carrasco Ochoa
National Institute of Astrophysics, Optics and Electronics
Luis Enrique Erro # 1, Santa María Tonantzintla, C.P. 72840, Puebla, México.
e–mail: ariel@inaoep.mx

Graduated in July 19, 2007

Abstract

The non–supervised classification algorithms determine clusters such that objects in the same cluster are similar among them, while objects in different clusters are less similar. However, there are some practical problems where, besides determining the clusters, the properties that characterize them are required. This problem is known as conceptual clustering. There are different methods that allow to solve the conceptual clustering problem, one of them is the conceptual k– means algorithm, which is a conceptual version of the k–means algorithm; one of the most studied and used algorithms for solving the restricted non–supervised classification problem (when the number of clusters is specified a priori). The main characteristic of the conceptual k–means algorithm is that it requires generalization lattices for the construction of the concepts. In this thesis, an improvement of the conceptual k–means algorithm and a new conceptual k–means algorithm that does not depend on generalization lattices for building the concepts are proposed. Finally, in this thesis, two fuzzy conceptual clustering algorithms, which are fuzzy versions of the proposed hard conceptual clustering algorithms, are introduced.

Keywords: Conceptual Clustering, Fuzzy Conceptual Clustering, Similarity Functions, Mixed Data.

Resumen

El estudio de la clasificación no supervisada ha sido enfocado principalmente a desarrollar métodos que determinen agrupamientos tales que objetos en el mismo agrupamiento sean similares entre ellos, mientras que objetos de diferentes agrupamientos sean poco similares. Sin embargo, para algunos problemas prácticos se requiere, además de determinar los agrupamientos, conocer las propiedades que describan cómo son dichos agrupamientos. A este problema se le conoce como agrupamiento conceptual. Existen diversos algoritmos que permiten resolver el problema de agrupamiento conceptual, entre los que se encuentra el algoritmo k–means conceptual, el cual es una versión conceptual del algoritmo k–means; uno de los algoritmos más estudiados y utilizados para resolver el problema de clasificación no supervisada restringida (cuando se especifica a priori el número de agrupamientos). La principal característica del algoritmo k–means conceptual es que requiere retículos de generalización para la construcción de los conceptos. En esta tesis se proponen dos algoritmos k–means conceptuales, el primero de ellos es una mejora del algoritmo k–means conceptual y el segundo es un algoritmo k–means conceptual que no requiere retículos de generalización para la construcción de los conceptos. Finalmente, en esta tesis se proponen dos algoritmos conceptuales difusos, los cuales son versiones difusas de los algoritmos conceptuales duros propuestos.

Palabras Clave: Agrupamiento Conceptual, Agrupamiento Conceptual Difuso, Funciones de Similaridad, Datos Mezclados.

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