不定値カーネルを伴うサポートベクターマシンに対するカーネル最適化  [in Japanese] A METHOD FOR SUPPORT VECTOR MACHINE CLASSIFICATION WITH INDEFINITE KERNELS  [in Japanese]

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Abstract

サポートベクターマシン(SVM)は2値分類問題を解くための手法である.SVMにおいて最も重要であるのは,適したカーネル行列の選び方であり,一般に半正定値のものが用いられる.しかし不定値のカーネル行列がデータの特性を表していることも多く,その場合のSVMのための様々な手法が考えられている.本論文では,その手法の一つであるLuss and d'Aspremondtのモデルを紹介し,その解法として射影勾配BB法を提案する.また,Lussらのモデルは計算量の点で問題があることから,その修正として新たなモデルを定式化し,数値実験により識別能力を評価する.

Support vector machines (SVMs) have been paid attention to for solving binary classification problems. SVMs usually use a positive definite kernels in many applications. On the other hand, SVMs with indefinite kernels are studied in this decade, because such SVMs take advantage of application-specific structure in data. Recently Luss and d'Aspremont (2009) formulated a convex optimization problem to deal with them. Their formula came from amax-min problem with a penalized term which controled the distance between the original indefinite kernel matrix and the proxy positive semidefinite kernel matrix. They gave a projected gradient method to solve the problem. However their method needs to calculate eigenvalues and vectors of a matrix corresponding to a given indefinite kernel matrix. In this paper, we first introduce the Barzilai and Borwein method instead of the gradient method of Luss and d'Aspremont to accelerate the method in practical computation. Secondly, we propose a new formulation of SVMs with indefinite kernels to overcome the defect that the model of Luss and d'Aspremont needs eigenvalues and vectors of a matrix. Since our formula is represented by a quadratic optimization problem, it can be easily solved by a suitable numerical method like the SMO method. Finally we give some numerical experiments to investigate numerical performance of our method and the generalization performance of our formulation.

Journal

  • Transactions of the Operations Research Society of Japan

    Transactions of the Operations Research Society of Japan 55(0), 110-131, 2012

    The Operations Research Society of Japan

References:  21

Codes

  • NII Article ID (NAID)
    110009578386
  • NII NACSIS-CAT ID (NCID)
    AA11998080
  • Text Lang
    JPN
  • Article Type
    ART
  • ISSN
    1349-8940
  • NDL Article ID
    024198994
  • NDL Call No.
    Z74-E331
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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