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- S. Hochreiter, M. Mozer,
and K. Obermayer. Coulomb Classifiers: generalizing Support Vector
Machines via an Analogy to Electrostatic Systems.
.
In Advances in Neural Information Processing Systems 15, pages
561-568, Cambridge, Massachusetts, 2003. MIT Press.
(FTP Gzipped PostScript, 8 pages, 178 kb)
We introduce a family of classifiers based on a physical analogy to
an electrostatic system of charged conductors. The family, called em
Coulomb classifiers, includes the two best-known support-vector machines
(SVMs), the nu--SVM and the C--SVM. In the electrostatics analogy, a
training example corresponds to a charged conductor at a given location in
space, the classification function corresponds to the electrostatic potential
function, and the training objective function corresponds to the Coulomb
energy. The electrostatic framework provides not only a novel interpretation
of existing algorithms and their interrelationships, but it suggests a
variety of new methods for SVMs including kernels that bridge the gap between
polynomial and radial-basis functions, objective functions that do not
require positive-definite kernels, regularization techniques that allow for
the construction of an optimal classifier in Minkowski space. Based on the
framework, we propose novel SVMs and perform simulation studies to show that
they are comparable or superior to standard SVMs. The experiments include
classification tasks on data which are represented in terms of their pairwise
proximities, where a Coulomb Classifier outperformed standard
SVMs.
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