On-line relational SOM for dissimilarity data

International audienceIn some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data

Self Organizing Map algorithm and distortion measure

International audienceWe study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an compact Euclidean space, we prove the strong consistency of the map which almost minimizes the empirical distortion. Moreover, after calculating the derivatives of the theoretical distortion measure, we show that the points minimizing this measure and the equilibria of the Kohonen map do not match in general. We illustrate, with a simple example, how this occurs

Injecting problem-dependent knowledge to improve evolutionary optimization search ability

The flexibility introduced by evolutionary algorithms (EAs) has allowed the use of virtually arbitrary objective functions and constraints even when evaluations require, as for real-world problems, running complex mathematical and/or procedural simulations of the systems under analysis. Even so, EAs are not a panacea. Traditionally, the solution search process has been totally oblivious of the specific problem being solved, and optimization processes have been applied regardless of the size, complexity, and domain of the problem. In this paper, we justify our claim that far-reaching benefits may be obtained from more directly influencing how searches are performed. We propose using data mining techniques as a step for dynamically generating knowledge that can be used to improve the efficiency of solution search processes. In this paper, we use Kohonen SOMs and show an application for a well-known benchmark problem in the water distribution system design literature. The result crystallizes the conceptual rules for the EA to apply at certain stages of the evolution, which reduces the search space and accelerates convergence. (C) 2015 Elsevier B.V. All rights reserved.Izquierdo Sebastián, J.; Campbell-Gonzalez, E.; Montalvo Arango, I.; Pérez García, R. (2016). Injecting problem-dependent knowledge to improve evolutionary optimization search ability. Journal of Computational and Applied Mathematics. 291:281-292. doi:10.1016/j.cam.2015.03.019S28129229