Extraction of representative subsets by potential funtion method and genetics algoritms

Abstract

Two procedures are suggested to select a representative subset from a large data set. The first is based on the use of the estimate of the multivariate probability density distribution by means of the potential functions technique. The first object selected for the subset is that for which the probability density is larger. Then, the distribution is corrected, by subtraction of the contribution of the selected object multiplied by a selection factor. The second procedure uses genetic algorithms to individuate the subset that reproduces the variance-covariance matrix with the minimum error. Both methods meet the requirement to obtain a representative subset, but the results obtained with the method based on potential functions are generally more satisfactory in the case when the original set is not a random sample from an infinite population, but is the finite population itself. Several examples show how the extraction of a representative subset from a large data set can give some advantages in the use of representation techniques (i.e., eigenvector projection, non-linear maps, Kohonen maps) and in class modelling techniques.