Neuroprose Paper: Classifiers on Relatively Compact Sets

[Ajit Dingankar]

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URL:
ftp://archive.cis.ohio-state.edu/pub/neuroprose/dingankar.relcompact-class.ps.Z

BiBTeX entry:
@ARTICLE{atd17,
	AUTHOR		= "Sandberg, I. W. and Dingankar, A. T.",
	TITLE		= "{Classifiers on Relatively Compact Sets}",
	JOURNAL		= "IEEE Transactions on Circuits
		 and Systems-I: Fundamental Theory and Applications",
	VOLUME		= {42},
	NUMBER		= {1},
	PAGES		= {57},
	YEAR		= "1995",
	MONTH		= "January",
	ANNOTE		= "",
	LIBRARY		= "",
	CALLNUM	        = ""
	}

		Classifiers on Relatively Compact Sets
		--------------------------------------

				Abstract

The problem of classifying signals is of interest in several
application areas.  Typically we are given a finite number $m$ of
pairwise disjoint sets $C_1, \ldots, C_m$ of signals, and we would
like to synthesize a system that maps the elements of each $C_j$ into
a real number $a_j$, such that the numbers $a_1,\ldots,a_m$ are
distinct.  In a recent paper it is shown that this classification can
be performed by certain simple structures involving linear functionals
and memoryless nonlinear elements, assuming that the $C_j$ are compact
subsets of a real normed linear space.  Here we give a similar
solution to the problem under the considerably weaker assumption that
the $C_j$ are relatively compact and are of positive distance from
each other.  An example is given in which the $C_j$ are subsets of $
\Lp(a,b), ~1 \le p < \infty $.