Coulomb's law yields support vector machines and more

[juergen@idsia.ch]

Important recent results by Sepp Hochreiter: Using Coulomb energy as
an objective function, he shows that support vector machines can be
easily derived from Coulomb's law as taught in first semester courses on
physics. His general electrostatic framework greatly simplifies the proofs
of well-known SVM theorems, and yields solutions formally identical to
well-known SVM types. In addition, it suggests novel kernels and SVMs for
kernels that are not positive definite, and even subsumes other methods
such as nearest neighbor classifiers, density estimators, clustering
algorithms, and vector quantizers. Thus his Coulomb classifiers promise
significant advances in several fields.

http://www.cs.tu-berlin.de/~hochreit
http://www.cs.colorado.edu/~hochreit
ftp://ftp.cs.colorado.edu/users/hochreit/papers/cltr.ps.gz

@techreport{Hochreiter:2001coulomb,
author = {S. Hochreiter and M. C. Mozer},
title = {Coulomb Classifiers: {R}einterpreting {SVM}s as 
Electrostatic Systems},
institution = {University of Colorado, Boulder, 
Department of Computer Science},
number = {CU-CS-921-01},
year = 	 {2001}}

(BTW, this is the same person who analyzed in rigorous detail the
vanishing error problem of standard recurrent nets (1991), and who
recently built the first working gradient-based metalearner (ICANN
2001) using LSTM recurrent nets (Neural Comp 97) which by design do
not suffer from this problem, and who also invented Flat Minimum Search
(Neural Comp 97, 99), a highly competitive method for finding nets with
low information-theoretic complexity and high generalization capability.)


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Juergen Schmidhuber                      director
IDSIA, Galleria 2, 6928 Manno-Lugano, Switzerland
juergen at idsia.ch            www.idsia.ch/~juergen