Feature Extraction Based On Tensor Framework

It is well known that feature extraction is one of the most basic and the most important problems in the field of pattern recognition.And extracting the effective features or key features is a shortcut for enhancing the recognition accuracy.Since there are only small numbers of high-dimensional training samples,how to extract the key features for dimensionality reduction and recognition is a hot topic with difficulties in current research in the image-based object recognition,particularly,in face recognition.Linear feature extraction is a basic method for feature extraction from face images.The basic idea of the linear feature extraction is to obtain a set of projections,by which the high-dimensional patterns are mapped on a low-dimensional subspace for getting the optimal intrinsic features under a certain criterion.This paper studies several classic face recognition methods.Inspired by the classic algorithms,we work out some new algorithms which can identify faces efficiently.The following are the main work and contributions of this paper:(1)This paper briefly introduces and summarizes the algebraic feature extraction technique which is wildly used.At the same time,the classical methods of algebraic feature extraction are introduced.Then,we introduce the basic multilinear algebra notations and present several linear regression models for obtaining sparse representations and their corresponding characteristics.(2)An improved algorithm based on Linear Discriminant Analysis(LDA)and Local Preserving Projection(LPP)is introduced in the paper.This algorithm is called Local Fisher Discriminant Analysis(LFDA).In this paper,a new multilinear approach Multilinear Local Fisher Discriminant Analysis(MLFDA)algorithm is proposed.Compared with traditional LFDA,this method preserves the image spatial structure.Experimental results on several face databases show that MLFDA algorithm has better recognition effect.(3)Based on the local Fisher discriminant analysis,a Multilinear Sparse Local Fisher discriminant analysis(MSLFDA)is proposed in this paper,which combines tensor framework and sparse representation.By using the idea in SPCA algorithm,MSLFDA transforms the MLFDA algorithm into linear regression problems.The algorithm not only makes the distance between the projective tensors as far as possible,but also keeps the resulting projection matrix sparse.A large number of experiments different face database show that MSLFDA has a better performance than the original MLFDA algorithm and SPCA algorithm.