Steepest descent method based LSSVM model

A new least square support vector machine SPLSSVM is constructed in the primal space, and the steepest descent method is designed to figure out the optimal solution by defining the optimal condition as the energy of the system. We rewrite the objective function by replacing the two norms of the slac...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1237; no. 5; pp. 52014 - 52020
Main Author Liang, Jinjin
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.06.2019
Subjects
Cholesky factorization
Norms
Optimization
Steepest descent method
Support vector machines
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Summary:A new least square support vector machine SPLSSVM is constructed in the primal space, and the steepest descent method is designed to figure out the optimal solution by defining the optimal condition as the energy of the system. We rewrite the objective function by replacing the two norms of the slack vector with the slack obtained from the equality constraints, and we derive an unconstrained optimization model. By setting gradient of the obtained objective function equal to zero, a linear system is derived. An energy function is defined and an interactive method is designed to figure out the optimal solution. The incomplete Cholesky factorization is used in the nonlinear space to approximate the kernel map before applying the steepest descent method. Numerical experiments demonstrate that the proposed SPLSSVM has higher precision and lower training time than SVM and LSSVM.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1237/5/052014