Loog Marco, Duin Robert P W
Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands.
IEEE Trans Pattern Anal Mach Intell. 2004 Jun;26(6):732-9. doi: 10.1109/TPAMI.2004.13.
We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chernoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chernoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented.
我们提出了一种基于特征向量的异方差线性降维（LDR）技术，用于多类数据。该技术基于一种异方差二类技术，该技术利用了所谓的切尔诺夫准则，并成功扩展了著名的线性判别分析（LDA）。后者基于费舍尔准则，无法以适当的方式处理异方差数据。对于二类情况，类间散度被推广，以便捕捉（协）方差的差异。结果表明，经典的类间散度概念可以与类均值之间的欧几里得距离相关联。从这个角度来看，通过采用切尔诺夫距离度量来推广类间散度，从而得到我们提出的异方差度量。最后，利用二类情况的结果，提出了切尔诺夫准则的多类扩展。该准则结合了类均值以及类协方差矩阵中存在的分离信息。本文还展示了广泛的实验以及与类似降维技术的比较。
