Department of Electrical and Computer Engineering, The Ohio State University, Columbus, 43210, USA.
IEEE Trans Pattern Anal Mach Intell. 2011 Mar;33(3):631-8. doi: 10.1109/TPAMI.2010.173.
Kernel mapping is one of the most used approaches to intrinsically derive nonlinear classifiers. The idea is to use a kernel function which maps the original nonlinearly separable problem to a space of intrinsically larger dimensionality where the classes are linearly separable. A major problem in the design of kernel methods is to find the kernel parameters that make the problem linear in the mapped representation. This paper derives the first criterion that specifically aims to find a kernel representation where the Bayes classifier becomes linear. We illustrate how this result can be successfully applied in several kernel discriminant analysis algorithms. Experimental results, using a large number of databases and classifiers, demonstrate the utility of the proposed approach. The paper also shows (theoretically and experimentally) that a kernel version of Subclass Discriminant Analysis yields the highest recognition rates.
核映射是将非线性分类器内在地推导出来的最常用方法之一。其思想是使用核函数将原始的非线性可分问题映射到一个固有维数更大的空间中，在这个空间中类是线性可分的。核方法设计中的一个主要问题是找到使问题在映射表示中线性化的核参数。本文导出了第一个专门旨在找到贝叶斯分类器成为线性的核表示的准则。我们说明了如何成功地将这一结果应用于几种核判别分析算法中。使用大量数据库和分类器的实验结果证明了所提出方法的实用性。本文还从理论和实验上表明子类判别分析的核版本可以产生最高的识别率。
