Research And Application Of Multi-set Canonical Correlation Analysis Based On Low Rank Theory

Canonical correlation analysis(CCA),as a classical feature extraction algorithm,can effectively extract the linear correlation between two sets of features,and has been widely used in various pattern recognition tasks.In order to integrate more pattern information,traditional CCA algorithm is generalized and multiset canonical correlation analysis(MCCA)is proposed.As a classic multi-feature extraction algorithm,CCA and MCCA have been widely used and studied.However,in the feature extraction of noise-containing data,the traditional CCA and MCCA are limited in their ability to represent features.Therefore,based on the low-rank decomposition theory,this paper integrates the low-rank decomposition step into the traditional canonical correlation analysis algorithm,and researches and validates the related algorithms.In this paper,the specific innovation and work are as follows:(1)Combining RPC A with CCA based on low-rank decomposition theory,a robust canonical correlation analysis(RbCCA)is proposed.In order to integrate more pattern information,RbCCA is generalized to extend,that is robust multiset canonical correlation analysis(RbMCCA).The validity of the proposed algorithm is demonstrated in the handwritten database and the face database,respectively.The experimental results show that the proposed RbCCA and RbMCCA algorithms are robust to noise data.(2)In order to overcome the restriction of feature recognition of unsupervised feature extraction algorithm,a robust discriminant canonical correlation analysis(RbDCCA)is proposed by combining low-rank decomposition and canonical correlation analysis.It is generalized to the multiset canonical correlation analysis,that is robust discriminant multisets canonical correlation analysis(RbDMCCA).Experiments show that the proposed algorithm is not only robust to noise,but also has stronger discrimination power than RbCCA and RbMCCA because it combines the class identification information.(3)Combining the class information of the samples,combining the low rank decomposition RPCA algorithm with the generalized canonical correlation analysis algorithm,robust generalized canonical correlation analysis algorithm(RbGCCA)is proposed.Robust generalized multisets canonical correlation analysis(RbGMCCA)is proposed for the generalized multiple generalizations.The validity of the new supervised extraction algorithm is proved by the experimental results on the experimental database.(4)RPCA algorithm is a transductive low-rank decomposition algorithm,that is,whenever the original training data in the database need to increase or delete part of the data,need to recalculate the new data low-order principal components and sparse noise components.This will undoubtedly increase the calculation time.Inductive robust principal component analysis(IRPCA)is combined with classical canonical correlation analysis and multiset canonical correlation analysis,a inductive robust canonical correlation analysis(IRbCCA)and inductive robust multiset canonical correlation analysis(IRbMCCA)is proposed.Inductive robust discriminant canonical correlation analysis(IRbDCCA)and inductive robust generalized canonical correlation analysis(IRbGCCA)are proposed by combining inductive principal component analysis with supervised canonical correlation analysis algorithm.We can obtain inductive robust discriminant multiset canonical correlation analysis(IRbDMCCA)and inductive robust generalized multiset canonical correlation analysis(IRbGMCCA)by generalizing them to the multiset theory of classical correlation analysis.