Department of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
IEEE Trans Pattern Anal Mach Intell. 1983 Jun;5(6):671-8. doi: 10.1109/tpami.1983.4767461.
A nonparametric method of discriminant analysis is proposed. It is based on nonparametric extensions of commonly used scatter matrices. Two advantages result from the use of the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired. This is in contrast to parametric discriminant analysis, which for an L class problem typically can determine at most L 1 features. Second, the nonparametric nature of the scatter matrices allows the procedure to work well even for non-Gaussian data sets. Using the same basic framework, a procedure is proposed to test the structural similarity of two distributions. The procedure works in high-dimensional space. It specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided. The nonparametric scatter matrices are also used to derive a clustering procedure, which is recognized as a k-nearest neighbor version of the nonparametric valley seeking algorithm. The form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm.
提出了一种非参数判别分析方法。它基于常用散度矩阵的非参数扩展。使用所提出的非参数散度矩阵有两个优点。首先，它们通常是满秩的。这提供了指定所需提取特征数量的能力。这与参数判别分析形成对比，参数判别分析对于 L 类问题通常最多可以确定 L1 个特征。其次，散度矩阵的非参数性质允许该过程即使在非高斯数据集上也能很好地工作。使用相同的基本框架，提出了一种用于检验两个分布结构相似性的过程。该过程在高维空间中工作。它指定了原始数据空间的线性分解，其中沿每个新基向量提供了不相似性的相对指示。非参数散度矩阵也用于导出聚类过程，它被认为是无参数山谷搜索算法的 k-最近邻版本。所得的形式提供了参数最近均值再分类算法和无参数山谷搜索算法的统一视图。
