TOPOGRAPHIC INDEPENDENT COMPONENT ANALYSIS: VISUALIZING THE DEPENDENCE STRUCTURE

Aapo Hyv#rinen, Patrik O. Hoyer and Mika Inki

In ordinary independent component analysis, the com­ ponents are assumed to be completely independent, and they do not necessarily have any meaningful or­ der relationships. In practice, however, the estimated iindependentj components are often not at all inde­ pendent. We propose that this residual dependence structure could be used to deøne a topographic order for the components. In particular, a distance between two components could be deøned using their higher­ order correlations, and this distance could be used to create a topographic representation. Thus we obtain a linear decomposition into approximately independent components, where the dependence of two components is approximated by the proximity of the components in the topographic representation.