The Out-of-Sample Problem Of Laplacian Eigenmaps And Regularized Dimensionality Reduction

Firstly,to solve the out?of?sample problem of Laplacian Eigenmaps,a method preserving local structure is proposed which is based on the assumption that there is a linear relationship between the new sample and its neighbors;then we utilize sparse?coding to obtain the linear reconstruction coefficients between the new sample and its neighbors.The low?dimensional representation of the new sample is computed through the linear relationship.Compared with sparse?coding reconstruction method based on global linear relationship,the method based on local information achieved higher accuracy using less time.Furthermore,the proposed method can be easily extended to the out?of?sample problem of other non?linear dimensionality reduction methods.Secondly,a supervised dimensionality reduction method with regularization is advanced to address the dimensionality reduction problem by learning from labels and high dimensional structure simultaneously.A two?stage optimization scheme proven to be solvable and convergent is adopted to solve the optimization problem.By comparison with other supervised dimensionality reduction algorithms,experiments demonstrated superiority of our method.