Fuzzy Relational Self-Organizing Maps

In this paper we propose a novel fuzzy relational self-organizing map algorithm (FRSOM) that can be used to map a set of n objects described by pairwise dissimilarity values to a two dimensional lattice structure. FRSOM generates a fuzzy membership matrix replacing the crisp best-matching unit matrix in the regular relational SOM (RSOM). We found that FRSOM discovers hard to find substructures in the data that present a challenge to the crisp relational SOM. Furthermore, we observed a triple relationship that seems to exist among the number of data points in the training data, map size and the fuzzifier m. We compare FRSOM and RSOM using several synthetic datasets.