Analytic center of spherical shells and its application to analytic center machine |
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Authors: | Fernanda M P Raupp B F Svaiter |
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Institution: | 1.Laboratório Nacional de Computa??o Científica—LNCC,Rio de Janeiro,Brazil;2.Instituto de Matemática Pura e Aplicada—IMPA,Rio de Janeiro,Brazil |
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Abstract: | The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points
with a good generalization performance.
In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses
the analytic center cutting plane method restricted to spherical shells.
In this work we prove existence and uniqueness of the analytic center of a spherical surface, which guarantees the well definedness
of ACM problem. We also propose and analyze new primal, dual and primal-dual formulations based on interior point methods
for the analytic center machine. Further, we provide a complexity bound on the number of iterations for the primal approach.
F.M.P. Raupp was partially supported by CNPq Grant 475647/2006-8 and FAPERJ/CNPq through PRONEX-Computational Modeling.
B.F. Svaiter was partially supported by CNPq Grants 300755/2005-8, 475647/2006-8 and by FAPERJ/CNPq through PRONEX-Optimization. |
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Keywords: | Pattern recognition problem Learning machines Interior point methods Analytic center |
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