Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3594
Title: TRAINING BINARY PERCEPTRONS BY CLIPPING
Authors: SCHIETSE, J
BOUTEN, Marcus 
VAN DEN BROECK, Christian 
Issue Date: 1995
Publisher: EDITIONS PHYSIQUE
Source: EUROPHYSICS LETTERS, 32(3). p. 279-284
Abstract: A teacher perceptron T with N binary components provides the classification of a set of p randomly chosen training examples. Several algorithms are available that use this information to select a student perceptron J with continuous components J(i). The purpose is to maximize the overlap R = T . J/(/T//J/), or to minimize the corresponding generalization error epsilon = (1/pi)arccos R. In view of the binary nature of the components of the teacher, one might expect that a lower error can be achieved by working with the clipped version of the student vector, namely the vector with components sign (J(i)). It turns out that this is not always the case. In this letter we calculate the overlap ($) over tilde R for a vector with components f(J(i)), where f can be any odd function of its argument, as a function of the overlap R. We show that the optimal choice of f is a hyperbolic tangent f(x) = th ((R/(1 - R(2))x)). The corresponding generalization error can go to zero exponentially fast in a(2), for a large (a = p/N).
Notes: SCHIETSE, J, LIMBURGS UNIV CENTRUM,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.
Document URI: http://hdl.handle.net/1942/3594
ISI #: A1995TC61000015
Type: Journal Contribution
Appears in Collections:Research publications

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