Emergence in Self Organizing Feature Maps

This paper sheds some light on the claim that Emergent SOM (ESOM) are different from other SOM. The discussion in philosophy and epistemology about Emergence is summarized in the form of postulates. The properties of SOM are compared to these postulates. SOM fulfill most of the postulates. The most critical of the postulates are those concerned with “the whole is more than the sum of its parts”. The epistemological postulates regarding this issue are hard, if not impossible, to prove. An alternative postulate relying on semiotic concepts, called “semiotic irreducibility” is proposed here. This concept is applied to U-Matrix on SOM with many neurons. This leads to the definition of ESOM as SOM producing a nontrivial U-Matrix on which the terms “watershed” and “catchment basin” are meaningful and which are cluster conform. It is demonstrated that a clustering algorithm (U*C) which exploits the emergent properties of such ESOM is superior to other popular clustering algorithms. Results on synthetic data in blind studies and a real world applications are convincing.