Kernel-Based Nonlinear Subspace Method for Pattern Recognition
Kernel-Based Nonlinear Subspace Method for Pattern Recognition
复制标题
基于核的非线性子空间模式识别方法
DOI：
10.1002/scj.1098
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
H. Murase
中科院分区：
文献类型：
--
作者：
Eisaku Maeda;H. Murase
提出了一种新的模式分类方法——基于核的非线性子空间（KNS）方法。它通过核函数定义的非线性变换实现了高维非线性空间中的子空间方法。支持向量机是一种采用核函数的非线性分类方法，具有先进的分类性能。然而，随着模式数量和类数量的增加，所面临的问题是学习所需的计算复杂性的爆炸式增长。传统的子空间方法是一种有效的多类分类器，是一种快速的分类技术。但是，如果模式分布是非线性的，或者特征空间的维数相对于类的数量较小，则无法获得令人满意的分类性能。该方法结合两种方法的优点，相互弥补不足，实现了分类性能高、计算复杂度低的多类非线性分类。在本文中，我们证明了使用核函数定义的非线性变换来表述非线性子空间方法的能力，并从非线性分布和多类分布的分类性能、分类性能相对于参数变化的稳定性以及学习和分类所需的计算成本等方面对所提出的方法进行了评价。并验证了该方法相对于传统方法的优越性。©2001 Scripta Technica, system Comp, 33(1): 38 - 52,2002
A new pattern classification method called the Kernel-based Nonlinear Subspace (KNS) method is proposed. It implements a subspace method in a high-dimensional nonlinear space by a nonlinear transformation defined by kernel functions. The Support Vector Machine, a recent popular current research topic, is a nonlinear classification method employing kernel functions and has advanced classification performance. However, as the number of patterns and the number of classes increase, the problem faced is an explosive increase in the computational complexity needed for learning. Conventional subspace methods are effective classifiers of multiple classes and are fast classification techniques. But satisfactory classification performance is not achieved if the pattern distribution is nonlinear or if the dimensionality of the feature space is small compared to the number of classes. The proposed method combines the advantages of both techniques to compensate for each other's deficiencies to realize nonlinear classification of multiple classes with advanced classification performance and low computational complexity. In this paper, we demonstrate the ability to use nonlinear transforms defined by kernel functions to formulate the nonlinear subspace method, evaluate the proposed method from the perspectives of classification performance for nonlinear distributions and multiclass distributions, the stability of the classification performance with respect to parameter variations, and the computational costs needed for learning and classification, and verify the superiority of the proposed method over conventional methods. © 2001 Scripta Technica, Syst Comp Jpn, 33(1): 38–52, 2002