Evolution of SOMs’ Structure and Learning Algorithm: From Visualization of High-Dimensional Data to Clustering of Complex Data

Marian B Gorzałczany,Filip Rudziński

doi:10.3390/a13050109

Abstract

In this paper, we briefly present several modifications and generalizations of the concept of self-organizing neural networks—usually referred to as self-organizing maps (SOMs)—to illustrate their advantages in applications that range from high-dimensional data visualization to complex data clustering. Starting from conventional SOMs, Growing SOMs (GSOMs), Growing Grid Networks (GGNs), Incremental Grid Growing (IGG) approach, Growing Neural Gas (GNG) method as well as our two original solutions, i.e., Generalized SOMs with 1-Dimensional Neighborhood (GeSOMs with 1DN also referred to as Dynamic SOMs (DSOMs)) and Generalized SOMs with Tree-Like Structures (GeSOMs with T-LSs) are discussed. They are characterized in terms of (i) the modification mechanisms used, (ii) the range of network modifications introduced, (iii) the structure regularity, and (iv) the data-visualization/data-clustering effectiveness. The performance of particular solutions is illustrated and compared by means of selected data sets. We also show that the proposed original solutions, i.e., GeSOMs with 1DN (DSOMs) and GeSOMS with T-LSs outperform alternative approaches in various complex clustering tasks by providing up to 20 % increase in the clustering accuracy. The contribution of this work is threefold. First, algorithm-oriented original computer-implementations of particular SOM’s generalizations are developed. Second, their detailed simulation results are presented and discussed. Third, the advantages of our earlier-mentioned original solutions are demonstrated.

Highlights

Self-organizing neural networks—usually referred to as self-organizing maps—were introduced in the beginning of 1980s by T
The objective of this paper is to briefly present several modifications and generalizations of the concept of self-organizing maps (SOMs)—starting from the simplest and ending with the most advanced ones—in order to illustrate their advantages in applications ranging from high-dimensional data visualization to complex data clustering
We demonstrated that the proposed original GeSOMs with 1DN (DSOMs) and GeSOMS with

Summary

Introduction

SOMs)—were introduced in the beginning of 1980s by T. Kohonen (see, e.g., [1,2]), who presented them as “a new, effective software tool for the visualization of high-dimensional data” (the quotation from Kohonen [1]). According to [4], “feature mapping is conceptually different from clustering” and the authors of [4] conclude that SOM “is not a clustering method, but which often lends ideas to clustering algorithms” (see a discussion in [5]). It is worth stressing that since the introduction of SOMs, their initial concept (including their structure and learning algorithm) has been significantly evolving and the range of its effective applications (including complex clustering problems) has been substantially broadened. SOMs constitute an active research field, see, Algorithms 2020, 13, 109; doi:10.3390/a13050109 www.mdpi.com/journal/algorithms

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