No subject

[Dan Kammen]

TOPIC:  PAPER FOR DISSEMINATION

WE HAVE RECENTLY COMPLETED AND SUBMITTED (N. NETWORKS) THE FOLLOWING
PAPER WHICH SHOULD BE OF INTEREST BOTH TO PERSONS MODELING
NEUROBIOLOGICAL NETWORKS AND THOSE DESIGNING SELF-ORGANIZING
ALGORITHMS:


	CORRELATIONS IN HIGH DIMENSIONAL OR ASYMMETRIC DATA SETS:
		     HEBBIAN NEURONAL PROCESSING

		WILLIAM R.SOFTKY and DANIEL M. KAMMEN  
            
		Computation and Neural Systems Program
       		  California Institute of Technology
                         Pasadena, CA 91125			

             	             ABSTRACT

The Hebbian neural learning algorithm that implements Principal
Component Analysis (PCA) can be extended for the analysis of more
realistic forms of neural data by including higher than 2-channel
correlations and non-Euclidean (l_P; l-sub-P) metrics.  Maximizing a
D-th rank tensor form which correlates D channels is equivalent to
raising the exponential order of variance correlation from 2 to D in
the algorithm that implements PCA.  Simulations suggest that a
generalized version of Oja's PCA neuron can detect such a D-th order
principal component.  Arguments from biology and pattern-recognition
suggest that neural data in general is not symmetric about its mean;
performing PCA with an implicit l_1 metric rather than the Euclidean
metric weights exponentially distributed vectors according to their
probability, as does a highly nonlinear Hebb rule.  The correlation
order D and the l_P metric exponent P were each roughly constant for
each of several Hebb rules simulated.  We propose and discuss a number
of these generalized correlation algorithms in terms of natural
(biological) and artificial network implementations.


Keywords: Principal Component Analysis, Hebbian learning,
self-organization, correlation functions, multi-dimensional
analysis, non-Euclidean metrics, information theory, asymmetric coding.

Address correspondence or preprint requests to:

Dr. D. M. KAMMEN:

Division of Biology, 216-76
California Institute of Technology
Pasadena, CA 91125 USA

kammen at aurel.cns.caltech.edu
KAMMEN at CALTECH.BITNET