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Abstract:
Independent component analysis of natural images leads to
emergence of simple cell properties, i.e. linear filters that
resemble wavelets or Gabor functions. In this paper, we extend ICA
to explain further properties of V1 cells. First, we decompose
natural images into independent subspaces instead of scalar
components. This model leads to emergence of phase and shift
invariant features, similar to those in V1 complex cells. Second,
we define a topography between the linear components obtained by
ICA. The topographic distance between two components is defined by
their higher-order correlations, so that the components are close
to each other in the topography if they are strongly dependent on
each other. This leads to simultaneous emergence of both topography
and invariances similar to complex cell properties.
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