二维典型相关分析的实质与改进算法

Essential of two-dimensional canonical correlation analysis and improved algorithm

由于样本数常小于样本维数,传统的典型相关分析方法CCA(canonical correlation analysis)会产生小样本问题。为了解决这类问题,一种新的有监督特征抽取方法——二维典型相关分析2DCCA被提出。与传统CCA方法把二维图像矩阵拉成一维向量不同,2DCCA直接从图像矩阵中抽取特征,该方法有效地解决了小样本问题。但是在单特征下,CCA的类标编码对识别率会产生影响,在一维情况下,传统的类标编码使得CCA等价于LDA,从而限制了CCA抽取更多有效的识别特征。证明了在传统的类标编码时,2DCCA仍然与2DI.DA等价。为了打破这种约束,提出了一种基于样本标号的2DCCA改进算法。在ORL和AR人脸库上的实验表明,提出的方法优于传统的2DCCA。

Traditional canonical correlation analysis （CCA） suffers the small sample size problem due to high matrix dimensions from the matrix-to-vector preprocessing. This problem was solved by a new supervised learning method called two-dimensional CCA （2DCCA）. The 2DCCA computed image covarianced matrix directly without matrix-to-vector conversion. But in one feature modality case, different encoding modes for class label could result in different classification performances. And CCA was equivalent to LDA in the traditional class-label encoding in 1-dimensional case which restricted the effective features extraction. Conclusion is drawn that the relationship between 2DCCA and 2DLDA is equivalent. In order to pro- mote the 2DCCA classification performance, an improved sample label-based 2DCCA was proposed. Experimental results on ORL and AR face databases show that the algorithm is better than the traditional 2DCCA in terms of the recognition performance.