Beta Scale Invariant Map

Abstract

In this study we present a novel version of the Scale Invariant Map (SIM) called Beta-SIM, developed to facilitate the clustering and visualization of the internal structure of complex datasets effectively and efficiently. It is based on the application of a family of learning rules derived from the Probability Density Function (PDF) of the residual based on the beta distribution, when applied to the Scale Invariant Map. The Beta-SIM behavior is thoroughly analyzed and successfully demonstrated over 2 artificial and 16 real datasets, comparing its results, in terms of three performance quality measures with other well-known topology preserving models such as Self Organizing Maps (SOM), Scale Invariant Map (SIM), Maximum Likelihood Hebbian Learning-SIM (MLHL-SIM), Visualization Induced SOM (ViSOM), and Growing Neural Gas (GNG). Promising results were found for Beta-SIM, particularly when dealing with highly complex datasets.