#### 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.