Canonical Correlation Analysis With Its Application

The analysis and processing of large-scale multimodal data is gradually playing an important role in the field of scientific research.In pattern classification,there are many large-scale multimodal data.These multimodal data are often of high dimensionality and very complicated to process.Therefore,efficient tools are needed to analyze and process these multi-modal data.Feature extraction is an effective method to process these data.Canonical correlation analysis plays an important role in feature extraction of multimodal data.On the basis canonical correlation analysis,researchers have proposed many related methods.However,these methods are not mature enough and have certain limitations.For example,the traditional canonical correlation analysis method is only suitable for linear structural data,and when the data dimension is too high,the traditional canonical correlation analysis results in over-fitting.In order to solve the over-fitting problem of traditional canonical correlation analysis,canonical correlation analysis based on sparse representation is proposed,but it cannot retain the original information of data.Aiming at the problems in traditional canonical correlation analysis and sparse canonical correlation analysis,this paper establishes a new canonical correlation analysis model.The main research work of this paper is as follows:Firstly,the basic theory and algorithm of canonical correlation analysis are introduced and several basic methods based on canonical correlation analysis are given.Then,the advantages and disadvantages of each method are listed,and the problem that sparse canonical correlation analysis cannot retain the original information of data is emphasized.Secondly,a new canonical correlation analysis optimization model,Trace Lasso sparse canonical correlation analysis,is proposed by using Trace Lasso norm.Trace lasso constraint penalty is applied to canonical vectors.When data correlation is strong,Trace Lasso regularization term is equivalent to 2-norm,which makes canonical variables retain original information as much as possible.When the data correlation is weak or irrelevant,the Trace Lasso regular term is equivalent to 1-norm,making the canonical vector sparse.In order to verify the performance of the new model,Simulation experiments are carried out on Yale face data set,ORL face data set and other data.The simulation results show that the new model algorithm is superior to other comparison algorithms.Thirdly,Trace Lasso sparse canonical correlation analysis only analyzes the correlation of two sets of variables.We extends the model to three or more sets of data and establishes Trace Lasso sparse multisett canonical correlation analysis model.A large number of experiments show that our method is superior to other methods.