Abstract: Canonical Correlation Analysis（CCA） is an important dimension reduction method for feature extraction by virtue of the correlation between samples.Correlation Discriminant Analysis（CDA） maximizes the correlation of the same class samples and minimizes the correlation between different class samples in the feature space，which can be treated as class-specific CCA.The feature extraction of the two methods is independent of the following classifier，i.e.the extracted features unnecessarily favor the classification.This independence affects the performance of classifiers unavoidably.In virtue of the characteristics that the vertices of the regular simplex are equidistant and affine invariant，use the vertices of the regular simplex to code the class labels so that the class information is incorporated in the classifier design.The algorithm，termed as Class-specific Correlation Multi-class Classifier（CCMC），maximizes the correlation between each sample and its class label，minimizes the correlation between each sample and the others class labels at the same time.Furthermore，this paper also proposes the corresponding kernelized version of CCMC by combining with the Empirical Kernel mapping，called as EK-CCMC.The experimental results on both artificial dataset and UCI benchmark datasets show that the proposed CCMC and EK-CCMC enhance the classifier performance by using class-specific correlation to design classifier.

Key words: Canonical Correlation Analysis（CCA）, linear discriminant analysis, feature extraction, class-specific, multi-class classifier design

摘要： 典型相关分析（CCA）是利用样本的相关性进行特征提取的一种重要的降维方法，而相关性判别分析（CDA）则是在特征空间中最大化同类样本对间的相关性，同时最小化不同类样本对间的相关性，可看作类依赖的典型相关分析。这两种方法的特征提取与其后的分类器是两个相互独立的过程，如此不可避免地会影响分类器的性能。借助正则单纯形的顶点等距并具有仿射不变性的特性，将其作为类标号编码，把样本中包含的类信息结合到分类器设计中，最大化各个样本与其类标号的相关性，同时最小化样本与其余类标号之间的相关性，得到类依赖的相关性多类分类器（CCMC）。进一步通过与经验核相结合，获得了具有更强分类性能的核化版非线性分类器EK-CCMC。人工数据集和部分UCI数据集上的实验结果表明，利用类依赖的相关性直接设计分类器可以提高分类性能。

关键词: 典型相关分析, 线性判别分析, 特征提取, 类依赖, 多类分类器设计