Separating capacity of analytic neurons
Adam P. Kowalczyk · 2002
This paper extends the classical results of T. Cover (1965) and others on separating capacity of families of nonlinear neurons of the form x/spl rarr/sgn (/spl Sigma//sub i=1//sup d/ /spl omega//sub i//spl phi//sub i/(x))=0, where w/sub i//spl isin/E are real coefficients (synaptic weights), /spl phi//sub i/:E/sup n//spl rarr/E are functions (measurement transformation) and sgn is the signum function on E. We show that the capacity of such a system is 2dim/spl phi/ input patterns, i.e. twice the number of linearly independent functions in the set /spl phi//sub 1/,.../spl phi//sub d/, if the functions /spl phi//sub i/ are analytic. This is achieved by showing that in such a case the Cover's assumption of /spl phi/-general positions of input vectors is almost universally satisfied.>