Face Recognition Based On Non-negative Matrix Factorization And Sparse Representation

As an important branch of biometric features recognition, face recognition hasbecome a hot research topic in the field of computer vision and obtains more and moreextensive attention. Many methods for face recognition have been presented byresearchers in succession, among which the appearance-based methods due to theirsimplicity, strong practicability and high efficiency, have become one of the highlightsin the field of face recognition. These methods usually include two importantprocedures, namely, feature extraction and classification. This paper mainly discussesNon-negative Matrix Factorization (NMF), which is a novel algorithm for featureextraction, and Sparse Representation based Classification (SRC), which is a novelclassifier.NMF is a new feature extraction algorithm. Due to the non-negative constraint,NMF can extract the local components of training samples. Besides, previous studieshave shown that the human brain’s perception of external things is based on theperception of the parts of the things. Therefore, NMF is connected to the human brain’sperception of external things. Thus algorithms for face recognition based on NMF havestrong practical values.In recent years, due to its advantages of high recognition rate and strongrobustness, face recognition methods based on sparse representation acquire more andmore attention from researchers. Unlike traditional subspace learning algorithms, sparserepresentation does not care about which feature is utilized for dimension reduction, butemphasizes sparsity and the design of classifier. Researches on sparse representationhave shown that if the classifier is appropriately designed, using what kind of feature fordimension reduction is no longer important. Therefore, face recognition based on sparserepresentation has introduced the research core of face recognition into the classifierdesign. Surrounding NMF and sparse representation, the innovative achievements andthe main work of this paper are as follows:A first novel approach called smoothness and principal components basednon-negative matrix factorization (SPNMF) is proposed in this paper. Through the studyof NMF, we found that the root cause of NMF’s slow convergence is that the base imagecontains a large amount of noise points. In addition, the correlation of the coefficientmatrix is quite big, which is not conducive to identify different images. In order to solve the above shortcomings of NMF, the SPNMF algorithm is proposed in this paper. Onthe one hand, we add a constant matrix to the base matrix to enhance its smoothness andstabilize the noise points, which causes to good convergence; On the other hand, thevariance between the different columns of the coefficient matrix as a penalty term isadded to the loss function of NMF for improving the discrimination of the coefficientmatrix. Experimental results on the PIE, AR and FERET face database have shown thatthe proposed SPNMF not only has higher recognition performance compared with NMF,but also is two to four times faster than the NMF.A second novel approach called two-dimensional nonnegative principalcomponent analysis (2DNPCA) is proposed in this paper. Through the study oftwo-dimensional principal component analysis (2DPCA), we found that2DPCA isbased on the whole images to preserve total variances by maximizing the trace offeature covariance matrix. However,2DPCA can not extract localized components,which are usually important for face recognition. Inspired by NMF, which is based onlocalized features, we integrate the nonnegative constraint into2DPCA and propose the2DNPCA algorithm.2DNPCA is a matrix-based algorithm to preserve the localstructure of facial images and has the nonnegative constraint to learn localizedcomponents. Therefore,2DNPCA has both advantages of2DPCA and NMF.Furthermore,2DNPCA solves the time-consuming problem by removing the restrictionof minimizing the cost function and extracting only the base matrix. Extensiveexperimental results on Yale, FERET, AR, and Extended Yale B four standard facedatabase show that2DNPCA is a very effective algorithm and is superior to2DPCA,2DLDA,2DLPP and NMF.A third novel approach called gradient-based sparse representation classification(GSRC) is proposed in this paper. Although sparse representation based on thel1-normandl2-norm have achieved promising classification results for face recognition fromfrontal views, they both require an overcomplete training dictionary, which is usuallyunrealistic. We focus on addressing the problem of performing face recognition basedon sparse representation with an incomplete dictionary. Motivated by the fact that imagegradients could explicitly consider the relationships between neighboring pixel pointsand be less sensitive to illumination than image pixels, we introduce image gradients tosparse representation and propose GSRC. By combining image pixels and imagegradients, GSRC has less model error and requires fewer training samples from eachindividual than SRC. Furthermore, GSRC can easily be combined with dimensionality reduction algorithms and be solved by the regularized least-square method, whichmakes GSRC work much faster than SRC. Extensive experimental results on Yale, AR,Extended Yale B and CMU PIE four standard face database demonstrate that GSRC isquite efficient for both incomplete dictionary and occlusion and has a reasonable speed.