Efficient Sparse Coding in Early Sensory Processing: Lessons from Signal Recovery
Figure 1
Different basis types of RPCA preprocessing and Sparse Coding.
Sample receptive fields are scaled into range [0,1]. (A) no RPCA, columns of dictionary . (B) receptive fields learned after PCA pre-filtering: features show wavy, global structure. (C) Features (‘global filters’) of the low dimensional signal for the case
(dimension = 17). (D) reverse correlation of the full rank sparsified signal
yields stereotypical DoG-like filters with symmetric 2D structure. The figure shows the profile of the central section as a function of
. At higher values the negative basin around the peak gets deeper. (E) Randomly selected sparse coding filter sets (over-completeness is
,
and
) With increasing
the filters get smaller and more localized (i.e. cleaner). (F) For comparison, a set of sparse coding filters (
) and the corresponding linear approximations (normalized reverse correlation,
) are shown at
.