A multiscale scheme for approximating the quantron's discriminating function

Authors:
Jean-François Connolly;Richard Labib
Affiliations:
LIVIA, Dept. of Automated Production, École de techn. supérieure, Montréal, QC, Canada and Dept. of Mathematical and Industrial Eng., École Polytechnique de Montréal, Mont ...;Department of Mathematical and Industrial Engineering, École Polytechnique de Montréal, Montréal, QC, Canada
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

Finding an accurate approximation of a discriminating function in order to evaluate its extrema is a common problem in the field of machine learning. A new type of neural network, the Quantron, generates a complicated wave function whose global maximum value is crucial for classifying patterns. To obtain an analytical approximation of this maximum, we present a multiscale scheme based on compactly supported inverted parabolas. Motivated by the Quantron's architecture as well as Laplace's method, this scheme stems from the multiresolution analysis (MRA) developed in the theory of wavelets. This approximation method will be performed, first, one scale at a time and, second, as a global approach. Convergence will be proved and results analyzed.