In ordinary independent component analysis, the components are assumed to b
e completely independent, and they do not necessarily have any meaningful o
rder relationships. In practice, however, the estimated "independent" compo
nents are often not at all independent. We propose that this residual depen
dence structure could be used to define a topographic order for the compone
nts. In particular, a distance between two components could be defined usin
g their higher-order correlations, and this distance could be used to creat
e a topographic representation. Thus, we obtain a linear decomposition into
approximately independent components, where the dependence of two componen
ts is approximated by the proximity of the components in the topographic re
presentation.