Sparsity Issues in Self-Organizing-Maps for Structures

Recent developments with Self-Organizing Maps (SOMs) produced methods capable of clustering graph structured data onto a fixed dimensional display space. These methods have been applied successfully to a number of benchmark problems and produced state–of–the–art results. This paper discusses a limitation of the most powerful version of these SOMs, known as probability measure graph SOMs (PMGraphSOMs), viz., the sparsity induced by processing a large number of small graphs, which prevents a successful application of PMGraphSOM to such problems. An approach using the idea of compactifying the generated state space to address this sparsity problem is proposed. An application to an established benchmark problem, viz., the Mutag dataset in toxicology will show that the proposed method is effective when dealing with a large number of small graphs. Hence, this work fills a gap between the processing of a number of small graphs, and the processing of densely connected graphs using PMGraphSOMs.