Fuzzy rough granular self-organizing map and fuzzy rough entropy

Abstract

A fuzzy rough granular self-organizing map (FRGSOM) involving a 3-dimensional linguistic vector and connection weights, defined in an unsupervised manner, is proposed for clustering patterns having overlapping regions. Each feature of a pattern is transformed into a 3-dimensional granular space using a π-membership function with centers and scaling factors corresponding to the linguistic terms low, medium or high. The three-dimensional linguistic vectors are then used to develop granulation structures, based on a user defined α-value. The granulation structures are labeled with integer values representing the crisp decision classes. These structures are presented in a decision table, which is used to determine the dependency factors of the conditional attributes using the concept of fuzzy rough sets. The dependency factors are used as initial connection weights of the proposed FRGSOM. The FRGSOM is then trained through a competitive learning of the self-organizing map. We also propose a new “fuzzy rough entropy measure”, based on the resulting clusters and using the concept of fuzzy rough sets. The effectiveness of the FRGSOM and the utility of “fuzzy rough entropy” in evaluating cluster quality are demonstrated on different real life datasets, including microarrays, with varying dimensions.