Patch Relational Neural Gas – Clustering of Huge Dissimilarity Datasets

Abstract

Abstract. Clustering constitutes an ubiquitous problem when dealing with huge data sets for data compression, visualization, or preprocessing. Prototype-based neural methods such as neural gas or the self-organizing map offer an intuitive and fast variant which represents data by means of typical representatives, thereby running in linear time. Recently, an extension of these methods towards relational clustering has been proposed which can handle general non-vectorial data characterized by dissimilarities only, such as alignment or general kernels. This extension, relational neural gas, is directly applicable in important domains such as bioinformatics or text clustering. However, it is quadratic in m both in memory and in time (m being the number of data points). Hence, it is infeasible for huge data sets. In this contribution we introduce an approximate patch version of relational neural gas which relies on the same cost function but it dramatically reduces time and memory requirements. It offers a single pass clustering algorithm for huge data sets, running in constant space and linear time only.

Parallelized Kernel Patch Clustering

“…For the k-approximation we simply determine the k samples that are nearest to their own cluster centre (prototype) and do that for each cluster l (as introduced in [7] for Relational Neural Gas):…”

“…Speed ups for the Kernel based methods to cluster large datasets have been done in Kernel K-Means [6] by block-wise calculating and processing the Kernel matrix which represents the similarities between the samples. In a recent scientific paper, Hasenfuss et al [7] have extended Guhas method furthermode with the Relational Neural Gas method (called Patch Relational Neural Gas) but restricted it for the time being to a sequential clustering procedure.…”

“…Our contribution in this paper is a generalization of the Patch Relational Neural Gas algorithm [7] to integrate multiple Kernel based clustering methods and call this algorithm simple the Kernel Patch Clustering (KPC) method. We additionally show the integration of Kernel Fuzzy C-Means and Kernel K-Means within the KPC method and the new assignment update formulas.…”