Probability Interpretation of Distributions on SOM Surfaces

In this paper, the distributions of training vectors on SOM surfaces are studied in terms of probabilities. The entropy of a single feature’s distribution and the mutual information of two features’ distributions are used to describe the form of the distributions quantitatively. Qualitatively different distributions can be obtained from the same data by using different feature extraction techniques and by studying different semantically related object subsets. In addition, the effect of low-pass filtering the SOM surfaces prior to the calculation of the entropy is studied. This technique facilitates analyzing the compactness and internal structure of an object class after mapping on the two-dimensional SOM surface. Illustrations and examples come from content-based image retrieval (CBIR), especially our PicSOM CBIR system.