Clustering biological data with SOMs: On topology preservation in non-linear dimensional reduction

Dimensional reduction is a widely used technique for exploratory analysis of large volume of data. In biological datasets, each object is described by a large number of variables (or dimensions) and it is crucial to perform their analyses in a smaller space, to extract useful information. Kohonen self-organizing maps (SOMs) have been recently proposed in systems biology as a useful tool for exploratory analysis, data integration and discovery of new relationships in *omics datasets. SOMs have been traditionally used for clustering in several data mining problems, mainly due to their ability to preserve input data topology and reduce a high dimensional input space into a 2-D map. In spite of this, the above-mentioned dimensional reduction can lead to counterintuitive results. Sometimes, maps having almost the same size, trained on the same dataset, and with identical learning algorithms and parameters, may find different clusters. However, one would expect that small changes in map sizes or another training condition would not result in an abrupt different location of any of the grouped patterns. The aim of this work is to analyze and explain this issue through a real case study involving transcriptomic and metabolomic data, since it might have an important impact when interpreting clustering results over a biological dataset.