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 dis- play space. These methods have been applied successfully to a number of bench- mark problems and produced state–of–the–art results. This paper discusses a limi- tation 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 estab- lished 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.