Characteristics of networks generated by kernel growing neural gas

TL;DR

This paper introduces kernel GNG, a kernelized version of the growing neural gas algorithm, and analyzes how different kernel parameters affect network properties like average degree and clustering coefficient.

Contribution

The study develops kernel GNG with five different kernels and investigates how kernel parameters influence network topology, providing insights into parameter selection.

Findings

Average degree decreases with increasing kernel parameter.

Clustering coefficient decreases as kernel parameter increases.

Larger kernel parameters favor sparser networks with fewer edges.

Abstract

This research aims to develop kernel GNG, a kernelized version of the growing neural gas (GNG) algorithm, and to investigate the features of the networks generated by the kernel GNG. The GNG is an unsupervised artificial neural network that can transform a dataset into an undirected graph, thereby extracting the features of the dataset as a graph. The GNG is widely used in vector quantization, clustering, and 3D graphics. Kernel methods are often used to map a dataset to feature space, with support vector machines being the most prominent application. This paper introduces the kernel GNG approach and explores the characteristics of the networks generated by kernel GNG. Five kernels, including Gaussian, Laplacian, Cauchy, inverse multiquadric, and log kernels, are used in this study. The results of this study show that the average degree and the average clustering coefficient decrease as the kernel parameter increases for Gaussian, Laplacian, Cauchy, and IMQ kernels. If we avoid more edges and a higher clustering coefficient (or more triangles), the kernel GNG with a larger value of the parameter will be more appropriate.