New Models And Fast Algorithms For Multi-view Canonical Correlation Analysis

Multi-view Canonical Correlation Analysis(MCCA)is a multi-view learning method,which has been widely used in data dimension reduction,image retrieval and other fields.SUMCOR is one of the most widely used approaches in multi-view canonical correlation analysis.There is an algorithm named Las CCA proposed recently for solving SUMCOR.However,Las CCA needs to solve many large-scale equations in each iteration,which costs a large amount of calculations.In this paper,we propose two algorithms to solve this problem.The first is a modified algorithm of Las CCA(Mod Las CCA).It is equivalent to Las CCA theoretically,which can reduce the number of large-scale equations.In order to reduce more costs,this algorithm can be used in inexact environment.The second is the Inverse-free Las CCA algorithm.It avoids solving large-scale equations and further reduces the calculation costs.Then we give some explanations based on the rationality of this model.For small-sample-size problems,Las CCA needs to select regularized parameters while there is no need in Inverse-free Las CCA.We consider uniqueness of the solution to Las CCA,and study the theory of stability and convergence.Theoretical results show that the Inverse-free Las CCA algorithm is more stable than the Las CCA algorithm.Numerical experiments indicate that our algorithms are efficient.Moreover,it is shown that the Inverse-free Las CCA algorithm is more suitable for recognition,while the Mod Las CCA algorithm is more useful for comparison of the correlation.