Large margin classifiers based on affine hulls

被引:34
|
作者
Cevikalp, Hakan [1 ]
Triggs, Bill [2 ]
Yavuz, Hasan Serhan [1 ]
Kucuk, Yalcin [3 ]
Kucuk, Mahide [3 ]
Barkana, Atalay [4 ]
机构
[1] Eskisehir Osmangazi Univ, Dept Elect & Elect Engn, TR-26480 Meselik, Eskisehir, Turkey
[2] Lab Jean Kuntzmann, Al Apprentissage & Interfaces Team, Grenoble, France
[3] Anadolu Univ, Dept Math, Eskisehir, Turkey
[4] Anadolu Univ, Dept Elect & Elect Engn, Eskisehir, Turkey
关键词
Affine hull; Classification; Convex hull; Kernel methods; Large margin classifier; Quadratic programming; Support vector machines; SUPPORT VECTOR MACHINES; ALGORITHMS; MANIFOLDS;
D O I
10.1016/j.neucom.2010.06.018
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper introduces a geometrically inspired large margin classifier that can be a better alternative to the support vector machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls. For any pair of classes approximated with affine hulls, we introduce two solutions to find the best separating hyperplane between them. In the first proposed formulation, we compute the closest points on the affine hulls of classes and connect these two points with a line segment. The optimal separating hyperplane between the two classes is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. The second formulation is derived by modifying the v SVM formulation. Both formulations are extended to the nonlinear case by using the kernel trick. Based on our findings, we also develop a geometric interpretation of the least squares SVM classifier and show that it is a special case of the proposed method. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed methods work as good as the SVM classifier if not any better. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:3160 / 3168
页数:9
相关论文
共 50 条
  • [41] Multiclass Graph-Based Large Margin Classifiers: Unified Approach for Support Vectors and Neural Networks
    Hanriot, Vitor M.
    Torres, Luiz C. B.
    Braga, Antonio P.
    IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2024,
  • [42] Learning Prototype-based Classifiers by Margin Maximization
    Wakou, Chiharu
    Kusunoki, Yoshifumi
    Tatsumi, Keiji
    2017 JOINT 17TH WORLD CONGRESS OF INTERNATIONAL FUZZY SYSTEMS ASSOCIATION AND 9TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (IFSA-SCIS), 2017,
  • [43] Margin-based diversity measures for ensemble classifiers
    Arodz, T
    COMPUTER RECOGNITION SYSTEMS, PROCEEDINGS, 2005, : 71 - 78
  • [44] Improved Design for Hardware Implementation of Graph-Based Large Margin Classifiers for Embedded Edge Computing
    Arias-Garcia, Janier
    de Souza, Alan Candido
    Gade, Liliane
    Yudi, Jones
    Coelho, Frederico
    Castro, Cristiano L.
    Torres, Luiz C. B.
    Braga, Antonio P.
    IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2024, 35 (01) : 1320 - 1329
  • [45] Using adaptively weighted large margin classifiers for robust sufficient dimension reduction
    Artemiou, Andreas
    STATISTICS, 2019, 53 (05) : 1037 - 1051
  • [46] Large-margin nearest neighbor classifiers via sample weight learning
    Hu, Qinghua
    Zhu, Pengfei
    Yang, Yongbin
    Yu, Daren
    NEUROCOMPUTING, 2011, 74 (04) : 656 - 660
  • [47] Average Margin Regularization for Classifiers
    Olfat, Matt
    Aswani, Anil
    2020 59TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2020, : 3194 - 3199
  • [48] Margin-Based Generalization Lower Bounds for Boosted Classifiers
    Gronlund, Allan
    Kamma, Lior
    Larsen, Kasper Green
    Mathiasen, Alexander
    Nelson, Jelani
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), 2019, 32
  • [49] Fast and Exact Leave-One-Out Analysis of Large-Margin Classifiers
    Wang, Boxiang
    Zou, Hui
    TECHNOMETRICS, 2022, 64 (03) : 291 - 298
  • [50] Distributed video surveillance using hardware-friendly sparse large margin classifiers
    Kerhet, Aliaksei
    Leonardi, Francesco
    Boni, Andrea
    Lombardo, Paolo
    Magno, Michele
    Benini, Luca
    2007 IEEE CONFERENCE ON ADVANCED VIDEO AND SIGNAL BASED SURVEILLANCE, 2007, : 87 - +