Catálogo de publicaciones - libros

The EM algorithm is a very powerful optimization method and has become popular in many fields. Unfortunately, EM is only a local optimization method and can get stuck in sub-optimal solutions. While more and more contemporary data/model combinations yield multiple local optima, there have been only very few attempts at making EM suitable for global optimization. In this paper we review the basic EM algorithm, its properties and challenges, and we focus in particular on its randomized implementation. The randomized EM implementation promises to solve some of the contemporary data/model challenges, and it is particularly well-suited for a wedding with global optimization ideas, since most global optimization paradigms are also based on the principles of randomization. We review some of the challenges of the randomized EM implementation and present a new algorithm that combines the principles of EM with that of the Genetic Algorithm. While this new algorithm shows some promising results for clustering of an online auction database of functional objects, the primary goal of this work is to bridge a gap between the field of statistics, which is home to extensive research on the EM algorithm, and the field of operations research, in which work on global optimization thrives, and to stimulate new ideas for joint research between the two.

Methods for fitting circles and spheres to point sets are discussed. LADAR (LAser Detection And Ranging) scanners are capable of generating ‘point clouds’ containing the () coordinates of up to several millions of points reflecting the laser signals. In particular, coordinates collected off objects such as spheres may then be used to model these objects by fitting procedures. Fitting amounts to minimizing what is called here a “gauge function,” which quantifies the quality of a particular fit. This work analyzes and experimentally examines the impact of the choice of three such gauge functions. One of the resulting methods, termed here as “algebraic” fitting, formulates the minimization problem as a regression. The second, referred to as “geometric” fitting, minimizes the sum of squares of the Euclidean distances of the data points from the tentative sphere. This method, based on orthogonal distance minimization, is most highly regarded and widely used. The third method represents a novel way of fitting. It is based on the directions in which the individual data points have been acquired.

In this paper, we apply the Analytic Hierarchy Process (AHP) to analyze why the New York Yankees signed Johnny Damon for $52 million over the next four years.