Canonical Correlation Analysis Based On Sparsity Preserving With Applications

With the development of science and technology, it is getting easier to get same data from a numberof different views, while the traditional machine learning methods mostly work on a view only. Inorder to take advantage of the correlation and complementary information of different views, peopleusually train classifiers independently and iteratively, and then verify whether the classification modelson independent data sets are effective. However, these methods use the complementary information onlyinstead of both. As one of multivariate statistical methods, Canonical correlation analysis (CCA) canreveal the linear relationship between two groups of multivariate data for multi-view feature extraction.What’s more, as sparse representation has been a hotspot of machine learning and pattern recognitionin reducing computational complexity and saving storage space, we introduce this idea into canonicalcorrelation analysis and propose a supervised multi-view learning method. Our major research work isas follows:Firstly, we propose sparsity preserving canonical correlation analysis (SPCCA). On one hand, ourmethod can select local information adaptively, by using sparsity preserving. On the other hand, classeinformation is embedded into the algorithm through calculating the weight matrix in samples of the sameclass, which makes it a supervised method. Besides, we introduce the idea of cross correlation whichenhances the relationship between unpaired samples of different views. And the algorithm is extendedto feature space through kernel trick, so that it can be able to handle more complex nonlinear situations.So, by taking advantage of classe information and corss correlation, SPCCA can not only extract relatedfeatures from two views, but also preserve as much discriminant information as possible. Experimentson toy problem, multi-character handwriting data set and ORL PIE YALE faces databases show theeffectiveness of our method.Secondly, we extend SPCCA to be able to handle unpaired samples situations, by using the ideaof intraclass correlation and interclass correlation. We design a series of experiments on toy problem,multi-character handwriting data set and YALE face database and apply our method on multi-modelclassification of medical images. From the experiments, we find our algorithm not only can extractfeatures and classify samples more effectively, but also robust to the number of missing samples.