Letters: Using Sequential Unconstrained Minimization Techniques to simplify SVM solvers

Authors:
Sachindra Joshi; Jayadeva;Ganesh Ramakrishnan;Suresh Chandra
Affiliations:
IBM Research - India, 4C, Vasant Kunj, New Delhi, India;Department of Electrical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India;Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai, India;Department of Mathematics, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, India
Venue:
Neurocomputing
Year:
2012

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Abstract

In this paper, we apply Sequential Unconstrained Minimization Techniques (SUMTs) to the classical formulations of both the classical L1 norm SVM and the least squares SVM. We show that each can be solved as a sequence of unconstrained optimization problems with only box constraints. We propose relaxed SVM and relaxed LSSVM formulations that correspond to a single problem in the corresponding SUMT sequence. We also propose a SMO like algorithm to solve the relaxed formulations that works by updating individual Lagrange multipliers. The methods yield comparable or better results on large benchmark datasets than classical SVM and LSSVM formulations, at substantially higher speeds.