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                     Designing a Sensory Processing System:
                            What Can Be Learned from
                         Principal Components Analysis?


                                 Ralph Linsker


                  IBM Research, T. J. Watson Research Center,
                           Yorktown Heights, NY 10598


          Principal  components analysis  (PCA) is  a useful  tool for
          understanding  some  feature-analyzing properties  of  cells
          found in at least the first few stages of a sensory process-
          ing pathway.  However, the relationships between the results
          obtained using PCA, and those obtained using a Hebbian model
          or an information-theoretic  optimization principle, are not
          as direct or clear-cut as sometimes thought.

          These points  are illustrated  for the formation  of center-
          surround  and  orientation-selective  cells.   For  a  model
          "cell" having spatially  localized connections, the relevant
          PCA eigenfunction problem is shown  to be separable in polar
          coordinates.  As  a result, the principal  components have a
          radially sectored  (or "pie-slice") geometric form,  and (in
          the absence  of additional  degeneracies) do  *not* resemble
          classic Hubel-Wiesel  "simple" cells,  except for  the (odd-
          symmetry) eigenmodes that have  exactly two sectors of oppo-
          site   sign.   However,   for   suitable  input   covariance
          functions, one  can construct  model "cells"  of simple-cell
          type --  which are in  general not PCA eigenfunctions  -- as
          particular  linear combinations  of  the  first few  leading
          principal components.

          A connection between  PCA and a criterion  for the minimiza-
          tion of a geometrically-weighted mean squared reconstruction
          error is also derived.

          This paper covers in greater detail  one of the topics to be
          discussed in an invited talk  at the IJCNN Winter 1990 Meet-
          ing (Washington,  DC, Jan. 1990).   It will be  published in
          the conference  proceedings.  The  paper itself  contains no
          abstract; the  above is  a brief  summary prepared  for this
          preprint availability notice.