Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2867
Title: Unsupervised learning of binary vectors: A Gaussian scenario
Authors: Copelli, M
VAN DEN BROECK, Christian 
Issue Date: 2000
Publisher: AMERICAN PHYSICAL SOC
Source: PHYSICAL REVIEW E, 61(6). p. 6971-6980
Abstract: We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry-breaking binary direction B epsilon {- 1, + 1}(N), Onto which the projections have a Gaussian distribution. We show that a candidate vector J undergoing Gibbs learning in this discrete space, approaches the perfect match J = B exponentially. In addition to the second-order "retarded learning" phase transition for unbiased distributions, we show that first-order transitions can also occur. Extending the known result that the center of mass of the Gibbs ensemble has Bayes-optimal performance, we show that taking the sign of the components of this vector (clipping) leads to the vector with optimal performance in the binary space. These upper hounds are shown generally not to be saturated with the technique of transforming the components of a special continuous vector, except in asymptotic limits and in a special linear case. Simulations are presented which are in excellent agreement with the theoretical results.
Notes: Univ Calif San Diego, Dept Chem & Biochem 0340, La Jolla, CA 92093 USA. Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium.Copelli, M, Univ Calif San Diego, Dept Chem & Biochem 0340, La Jolla, CA 92093 USA.
Document URI: http://hdl.handle.net/1942/2867
DOI: 10.1103/PhysRevE.61.6971
ISI #: 000087575400034
Category: A1
Type: Journal Contribution
Validations: ecoom 2001
Appears in Collections:Research publications

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