Efficient Revised Simplex Method for SVM Training

    Authors

    C. Sentelle; G. C. Anagnostopoulos;M. Georgiopoulos

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Neural Netw.

    Keywords

    Active set method; null space method; quadratic programming; revised; simplex method; support vector machine; SUPPORT VECTOR MACHINES; Computer Science, Artificial Intelligence; Computer Science, Hardware &; Architecture; Computer Science, Theory & Methods; Engineering, ; Electrical & Electronic

    Abstract

    Existing active set methods reported in the literature for support vector machine (SVM) training must contend with singularities when solving for the search direction. When a singularity is encountered, an infinite descent direction can be carefully chosen that avoids cycling and allows the algorithm to converge. However, the algorithm implementation is likely to be more complex and less computationally efficient than would otherwise be required for an algorithm that does not have to contend with the singularities. We show that the revised simplex method introduced by Rusin provides a guarantee of nonsingularity when solving for the search direction. This method provides for a simpler and more computationally efficient implementation, as it avoids the need to test for rank degeneracies and also the need to modify factorizations or solution methods based upon those rank degeneracies. In our approach, we take advantage of the guarantee of nonsingularity by implementing an efficient method for solving the search direction and show that our algorithm is competitive with SVM-QP and also that it is a particularly effective when the fraction of nonbound support vectors is large. In addition, we show competitive performance of the proposed algorithm against two popular SVM training algorithms, SVMLight and LIBSVM.

    Journal Title

    Ieee Transactions on Neural Networks

    Volume

    22

    Issue/Number

    10

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    1650

    Last Page

    1661

    WOS Identifier

    WOS:000295584100012

    ISSN

    1045-9227

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