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NeuroCOLT
Technical Report NC-TR-96-028
Threshold Functions,
Decision Lists, and the Representation of Boolean Functions
Martin
Anthony
London School of Economics
UK
Abstract
We describe a geometrically-motivated technique for data classification.
Given a finite set of points in Euclidean space, each classified according
to some target classification, we use a hyperplane to separate off
a set of points all having the same classification; these points are
then deleted from the database and the procedure is iterated until
no points remain. We explain how such an iterative `chopping procedure'
leads to a type of decision list classification of the data points
and in a classification of the data by means of a linear threshold
artificial neural network with one hidden layer. In the case where
the data points are all the $2^n$ vertices of the Boolean hypercube,
the technique produces a neural network representation of Boolean
functions differing from the obvious one based on a function's disjunctive
normal formula.
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