Javier Trejos

RESUMEN El propósito de este artículo es presentar los resultados de la evaluación de heurísticas de optimización combinatoria por particiones, específicamente, sobrecalentamiento simulado, búsqueda tabú y algoritmos genéticos, en comparación con métodos tradicionales como k-medias y clasificación jerárquica de Ward. Se utilizaron tablas de datos generadas al azar de acuerdo con ciertos parámetros establecidos. Se generaron 16 tablas de datos con variables normalmente distribuidas, se repitió el experimento 100 veces para cada tabla y cada método, y como parámetro de comparación de los resultados se utilizó la inercia intra-clases (W). Los mejores resultados se obtuvieron para el sobrecalentamiento simulado y el algoritmo genético. ABSTRACT The aim of this paper is to present the results of the evaluation of combinatorial optimization heuristic applied to obtain partitions in clustering: simulated annealing, tabu search and a genetic algorithm, using data tables generated randomly a...

RESUMEN En este artículo se estudian diversos enfoques para definir promedios móviles y volatilidades desde el punto de vista exponencial, es decir, dando mas ponderación a los datos mas recientes. Se ve que varios de los que enfoques usados en la literatura adolecen de varios problemas de definición. Se propone una manera de definir un sistema completo de pesos y de esta manera corregir algunos de los problemas que presentan esos enfoques. Además, se propone una fórmula recurrente que converge al promedio móvil y la volatilidad exponencial reales. Finalmente, se estudian las cotas para los errores de aproximación que se cometen cuando se usan las fórmulas estudiadas. ABSTRACT: In this paper different approaches are studied, for defining moving averages and volatiles from the exponential point of view that is, giving a larger weight to the more recent data. It is obtained that different approaches, appearing in the literature, have different definition problems. A method is proposed...

Hemos desarrollado el algoritmo usual de clasificacion jerarquica ascendente en el sistema MATHEMATICA. El usuario escoge la disimilitud segun el tipo de datos que deba analizar: cuantitativos, cualitativos o binarios, asi como el indice de agregacion a utilizar. Se dispone de varias opciones para cada escogencia. Ademas, se ha implementado un gran numero de manipulaciones sobre el arbol binario de clasificacion, como el corte del arbol, la rotaciones, la dimensionalidad, el etiquetado, los colores, etc.

We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization metaheuristics: first ones are simulated annealing, threshold accepting and tabu search, and the others are a genetic algorithm and ant colony optimization. The methods are implemented, performing the proper calibration of parameters in the case of heuristics, to ensure good results. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM. Simulated annealing perform very well, especially compared to classical methods.

The term structure of interest rates or yield curve is a function relating the interest rate with its own term. Nonlinear regression models of Nelson-Siegel and Svensson were used to estimate the yield curve using a sample of historical data supplied by the National Stock Exchange of Costa Rica. The optimization problem involved in the estimation process of model parameters is addressed by the use of four well known combinatorial optimization metaheuristics: Ant colony optimization, Genetic algorithm, Particle swarm optimization and Simulated annealing. The aim of the study is to improve the local minima obtained by a classical quasi-Newton optimization method using a descent direction. Good results with at least two metaheuristics are achieved, Particle swarm optimization and Simulated annealing. Keywords: Yield curve, nonlinear regression, Nelson-

We study some criteria that can be applied for the partitioning of a set of objects when non Euclidean distances are used; particularly, these criteria can be used when the data are described by binary variables. These criteria are based on aggregations that measure the homogeneity of a class and some are generalizations of variance or inertia. Properties of the criteria are studied and partitioning methods are proposed, based on metaheuristics of global optimization, such as simulated annealing and tabu search. Finally, comparative results on binary data are shown. RESUMEN Se estudian criterios que se pueden aplicar para particionar un conjunto de objetos cuando se usan distancias no euclídeas; en particular, los criterios pueden ser usados cuando los datos son descritos por variables binarias. estos criterios están basados en agregaciones que miden la homogeneidad de una clase y algunos son generalizaciones de la varianza o inercia. Se estudian algunas de las propiedades de los cr...

Se desarrolla la teoría necesaria para realizar el Análisis de Datos en presencia de semiproductos escalares, extendiendo los conceptos clásicos de productos escalares usualmente empleados. Para ello, retomamos las definiciones algebraicas básicas de las formas bilineales no degeneradas y vamos desarrollando todas las herramientas algebraicas necesarias. Se estudian los operadores m´as importantes en el espacio de
individuos, como el operados VM y el operador MV . También se estudia el caso del semiproducto escalar de pesos en el espacio de variables, que en el caso de pesos nulos corresponde a la introducci´on de individuos suplementarios. Finalmente, llegamos a los conceptos usuales del Análisis en Componentes Principales.

Abstract.
We develop the theory necessary for Data Analysis with inner semiproducts, extending tha classical concepts of inner products usually employed. For this, we use
the basic algebraic definitions of non degenerated bilinear forms and develop all the
algebraic tools needed. We study the most important operators on the individual
space, such as the V M and the MV operators. We also study the case of the inner
semiproduct of weights in the variable space, which corresponds to the introduction of
supplementary individuals in the case of null weights. Finally, we arrive to the usual
concepts of Principal Component Analysis.

An index of soil quality and health for banana plantations in four countries of Latin America and the Caribbean The productivity of banana plantations in several Latin America and Caribbean countries has shown significant declines over the past decade which has been associated with a deterioration of physical, chemical and biological soil factors. This study aimed to construct a mathematical index to describe the quality and health of these soils, indicating the most critical factors in production. Sixty-six indicators were measured in 38 selected banana farms with different levels of production in Costa Rica, Dominican Republic, Panama and Venezuela. Discriminant analysis for all of the countries indicated that the explanatory variables of discrimination are quite different among the countries, so we proceeded to define individually the quality and health indices. Seventeen indicators were identified for Costa Rica, 13 for Panama, 11 for Venezuela and 22 from Dominican Republic; th...

The term structure of interest rates or yield curve is a function relating the interest rate with its own term. Nonlinear regression models of Nelson-Siegel and Svensson were used to estimate the yield curve using a sample of historical data supplied by the National Stock Exchange of Costa Rica. The optimization problem involved in the estimation process of model parameters is addressed by the use of metaheuristics: Ant colony, Genetic algorithm, Particle swarm and Simulated annealing. The aim of the study is to improve the local minimum obtained by an optimization method using descent direction. Good results with at least two metaheuristics are achieved, Particle swarm and Simulated annealing.

RESUMEN Se presenta un estudio de los principales métodos de clasificación bimodal, tanto jerárquica como por particiones. Se propone una fórmula de recurrencia del tipo Lance & Williams para la clasificación jerárquica bimodal, usando el criterio de ...

... J) was choosen in the previous step, make a transfer A/,-V Ay (resp. BI A By) in the following way: choose at ran-dom a row i 6 7 (resp. a column j€ J) of X, choose at random a first-mode class k'(resp. a second-mode class/') different from the current class k (resp. I) of i (resp. ...

On propose una méthode de classification par partitions qui utilise la technique de la recherche tabou, basée sur les transferts, afin d’obtenir des classes bien séparées entre elles et les plus homogènes. L’algorithme proposé fait une recherche dirigée afin de trouver la partition optimale du critère de l’inertie intra-classes. On montre le fonctionnement de l’algorithme sur un exemple simple.

Usual methods for solving some Multivariate Data Analysis problems, like partitioning in clustering, metric multidimensional scaling (MDS) and non-linear regression (NLR), find local optima of the criteria they minimize. Recently, many general optimization heuristics, called metaheuristics, have ben proposed to find global optima of discrete optimization problems. Between these heuristics, are simulated annealing (SA), tabu search (TS), genetic algorithms (GA), ant colonies (ACO) and particle swarms (PSO). For this reason, several authors have tried to find better solutions to Data Analysis problems using metaheuristics of optimization. The team of research PIMAD1 in the Research Center for Pure and Applied Mathematics (CIMPA) at the University of Costa Rica has tackled the application of modern combinatorial optimization heuristics in some of those Multivariate Data Analysis problems. The PIMAD team has been integrated by: Eduardo Piza, William Castillo, Jorge González, Mario Villalobos, Alex Murillo, Javier Trejos, Oldemar Rodríguez and Carlos Arce. We have collaborated with colleagues of other universities, like José Luis Espinoza, Geovanni Figueroa and Walter Mora from the Technological Institute of Costa Rica, and Sergio de los Cobos and John Goddard, from the Metropolitan Autonomous University, campus Iztapalapa, in Mexico. Table 1 summarizes the problems that have been tackled at the PIMAD, in association with some other colleagues of the Central American and Caribbean Society of Classification and Data Analysis (SoCCCAD).

We apply tabu search, as an optimization heuristic, to the problem of two-mode clustering for minimization of the two-mode variance criterion. States are two-mode partitions, neighborhoods are defined by transfers of a single row or column-mode object into a new class, and the tabu list contains the values of the criterion. We compare the results obtained with those of other methods, such as alternating exchanges, k-means, simulated annealing and a fuzzy-set approach.

We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization metaheuristics: first ones are simulated an-nealing, threshold accepting and tabu search, and the others are a genetic algorithm and ant colony optimization. The methods are implemented, performing the proper calibration of parameters in the case of heuris-tics, to ensure good results. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM. Simulated annealing perform very well, especially compared to classical methods.