基于低秩分解的鲁棒典型相关分析

Robust canonical correlation analysis based on low rank decomposition

典型相关分析(CCA)是一种经典的多特征提取算法,它能够有效地抽取两组特征之间的相关性,现已被广泛应用于模式识别。在含噪声数据情况下,CCA的特征表示性能受到限制。为了使CCA更好地处理含噪声数据,提出一种基于低秩分解的典型相关分析算法——鲁棒典型相关分析(robust canonical correlation analysis,Rb CCA)。Rb CCA首先对特征集进行低秩分解,得到低秩分量和噪声分量,以此分别构建对应的协方差矩阵。通过最大化低秩分量的相关性,同时最小化噪声分量的相关性来建立判别准则函数,进而求取鉴别投影矢量。在MFEAT手写体数据库、ORL和Yale人脸数据中的实验结果表明,在包含噪声的情况下,Rb CCA的识别效果优于现有的典型相关分析方法。

Canonical correlation analysis （CCA） is a popular multi-feature extraction method, which can effectively explore the correlations between two sets of features. Up to now, CCA has been widely used in pattern recognition, however it has limited feature extraction power for large noisy data. For CCA to deal better with noisy data, a new method, robust canonical correlation analysis （RbCCA） , based on low rank decomposition, is proposed. RbCCA first decomposes features using low rank decomposition to get the low rank and noisy components, then it constructs new eovarianee matrices based on these two components. A discriminative criteria function is further established to obtain discriminative projections by maximizing the correlations of the low rank component and minimizing the correlations of the noisy component. Experimental results on a MFEAT handwritten dataset, and ORL and Yale face datasets show that RbCCA can achieve higher recognition rates than existing CCA methods, especially in noisy settings.