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Doctoral thesis Nowadays, knowledge extraction from data is an essential task for decisionmaking in many areas. However, the data sets commonly present some negative problems (complexities) that decrease the performance in the knowledge extraction process. The imbalanced distribution of data between classes and the presence of noise and/or class overlap are data intrinsic characteristics that frequently decrease the performance of the knowledge extraction because data are assumed to keep a uniform distribution and free from any other problem. All these issues have been studied in Pattern Recognition and Data Mining, because of their impact on the performance of the learning models. Thus this Ph.D. thesis addresses class imbalance, class overlap and/or noise through techniques that reduce and clean the most represented class. Among the solutions to handle with the class imbalance problem, new algorithms based on graphs are proposed. This idea arises from the fact that many real-world problems (network analysis, chemical models, remote sensing, among others) have been tackled by using graph-based strategies, in which the problem is transformed in terms of vertices and edges. Keeping this in mind, the proposals presented in this Ph.D. thesis consider the most represented class as as a complete graph in such a way that a representative subset of majority class instances is obtained through reduction criteria. Regarding the data sets with class imbalance and class overlap and/or noise, the proposals include the use of clustering algorithms as a cleaning strategy. It is well known that these algorithms are used to group instances according to similar characteristics; however, the proposal here presented makes use of their ability to detect noisy instances. By this, the application of a clustering algorithm is carried out before facing the class imbalance. As a further extension to the proposals presented in this Ph.D. thesis and due to the growing interest in Big Data problems, the last part of this report introduces a graph-based algorithm to handle class imbalance in large-scale data sets. Becas nacionales del CONACYT

espanolLa presente Tesis se centra en el desarrollo del Analisis de Arquetipos (AA) y demuestra su viabilidad y rigor. Amplia la tipologia de datos con las que puede trabajar utilizando, ademas de los datos multivariantes continuos, datos binarios y datos funcionales. Hemos trabajado esta amalgama de datos, implementando AA en diferentes bases de datos, dando como fruto tres investigaciones independientes. En la primera aportacion trabajamos resultados de examenes utilizando una variante de AA, el Analisis de Arquetipoides (ADA) con datos binarios y funcionales, en la segunda aportacion presentamos un algoritmo basado en AA para trabajar la segmentacion de texturas y en la ultima presentamos otro algoritmo para la busqueda de datos atipicos (outliers). En todas estas investigaciones, se han utilizado datos reales y se ha hecho un estudio comparativo con otros analisis y algoritmos mas reconocidos. Los resultados obtenidos han demostrado con creces la viabilidad y la competencia de AA. EnglishThis Thesis develops the Archetype Analysis (AA) and demonstrates its viability and rigor. Expands the type of data which can work with, in addition to continuous multivariate data, it will manage binary data and functional data too. This amalgam of data will be used by implementing AA in different databases, resulting in three independent investigations. In the first contribution we work out exam results using a variant of AA, Archetypoids Analysis (ADA) with binary and functional data, in the second contribution we present an AA-based algorithm to work on texture segmentation and in the last one we present another algorithm for the search outliers. In all these investigations, real data have been used and a comparative study has been done with other more recognized analyzes and algorithms. The results obtained have demonstrated the AA feasibility and competence. catalaAquesta Tesi desenvolupa l’Analisi d’Arquetipus (AA) i demostra la seua viabilitat i rigor. Amplia la tipologia de dades amb les quals pot treballar utilitzant, a banda de les dades multivariants continues, dades binaries i dades funcionals. Aquesta amalgama de dades l’hem treballat implementant AA en diferents bases de dades, donant com a fruit tres investigacions independents. En la primera aportacio treballem resultats d’examens utilitzant una variant d’AA, l’Analisi d’Arquetipoids (ADA) amb dades binaries i funcionals, en la segona aportacio presentem un algorisme basat en AA per a treballar la segmentacio de textures i en la darrera presentem un altre algorisme per a la cerca de dades atipiques (outliers). En totes aquestes investigacions, s’han utilitzat dades reals i s’ha fet un estudi comparatiu amb altres analisis i algorismes mes reconeguts. Els resultats obtinguts han demostrat amb escreix la viabilitat i la competencia d’AA.

Esta tesis se centra principalmente en el desarrollo de propiedades y características de los estimadores de segundo orden de procesos puntuales y espacio-temporales. En primer lugar, se presenta un marco teórico acerca de procesos puntuales espaciales y espacio-temporales. El resto de la tesis se organiza como sigue. En el capítulo 2, se presenta una nueva familia de kernel positivos y óptimos, además se propone un estimador insensgado alternativo para la función de la densidad del producto. Su rendimiento se compara para varios kernel mediante MISE. En el capítulo 3, se dada un nuevo estimador kernel de la función de la densidad producto espacio-temporal y también se desarrollan expresiones cerradas para la varianza en el caso de Poisson. En el Capítulo 4, nos centramos en los métodos de orientación de segundo orden los cuales proporcionan una herramienta para el análisis natural para los datos espaciales anisótropicos. Finalmente, se proporciona una descripción general de los proyectos de investigación actualmente en curso que han surgido motivadas por la estrecha relación con las propiedades de segundo orden de los procesos puntuales espaciales y espacio-temporales., This thesis is mainly focused on developing properties and estimators for second-order characteristics of spatio-temporal point processes. First, we present a theoretical framework of spatial and spatio-temporal point processes. The rest of the thesis is organized as follows. In Chapter 2 we present a new family of optimal and positive kernels an alternative unbiased estimator for the product density function. Its performance is compare under several kernel through MISE. In Chapter 3 a new kernel estimator of spatio-temporal product density function are given and also are developed close expressions for the variance under the Poisson case. En el capítulo 4 nos centramos en los métodos de orientación de segundo orden que proporcionan una herramienta natural para el análisis de los datos de proceso Punto espaciales anisótropas. Finally, we provide a general description of the currently ongoing research projects which have emerged motivated by the close relationship with the second-order properties.