Relational Fuzzy Self-Organizing Maps for Cluster Visualization and Summarization

Abstract

The notion of Best-Matching Unit (BMU) in the proposed Fuzzy Relational Self-Organizing (FRSOM) algorithm is replaced by a membership function where every neuron has a certain degree of matching to an input object. The FRSOM is an extension of the relational self-organizing map. In the proposed FRSOM we incorporate a monotonically increasing fuzzifier and a monotonically decreasing neighborhood kernel. Initially, FRSOM assigns winning neurons. However, as time progresses adjacent neurons begin communicating and sharing information about the stimulus received. The amount of information being shared at a given time is governed by the fuzzifier and the number of neurons sharing information is controlled by the neighborhood kernel. Additionally, in this paper we show that FRSOM is the relational dual of Fuzzy Batch SOM (FBSOM) followed by experimental results comparing both FBSOM and FRSOM on synthetic datasets. Then we will demonstrate the visualization and summarization capabilities of FRSOM on two real relational datasets, Gene Ontology and a patient data consisting of Activity of Daily Living score trajectories.