Research On Nuclear Norm Based Feature Extraction And Face Recognition

The technology of face recognition is becoming a hot issue in pattern recognition and machine learning field. How to extract effective feature is the key point in face recognition. Till now, people have proposed a lot of algorithms about feature extraction. These algorithms approximately can be divided into two groups:the one type is linear feature extraction, the other one is non-linear feature extraction. The most classic linear feature extractions include principal component analysis (PCA), linear discriminant analysis (LDA). Their main idea is to find a linear transform projection matrix. As to non-linear feature extraction, including kernel principal component analysis (KPCA), kernel linear discriminate analysis (KLDA), locality preserve projection (LPP), marginal fisher analysis (MFA). All of these algorithms mentioned above are based on Euclidean norm which is less robust to noise. Trying to avoid the influence which is caused by noise (such as light or shade), people propose the idea based on nuclear norm. They use nuclear norm instead of F-norm to measure the distance between the samples. We have a very deep research on feature extraction based on nuclear norm. The extensive experimental results will demonstrate the effectiveness of them. The main work for this thesis can be summarized as follows:1、Nuclear Norm Based Bidirectional 2DPCAClassic two-dimensional principle component analysis uses F-norm to measure the error between samples and reconstruction. But F norm is less robust to the noise caused by light, shade and occlusion. So we develop a new image feature extraction and recognition method coined bidirectional compressed nuclear-norm based 2DPCA (BN-2DPCA). BN-2DPCA presents a sequentially optimal image compression mechanism, making the information of the image compact into its up-left corner. Due to the use of nuclear norm, we redefine the objective function so that we reduce the influence of illumination and then transform the nuclear norm optimization problem into a serial of F-norm optimization problem. BN-2DPCA is tested using the Extended Yale B and the CMU PIE face databases. The experimental results show BN-2DPCA is more effective than N-2DPCA, B2DPCA, LPP and LDA for face feature extraction and recognition.2、Nuclear Norm based Graph Regularization Non-Negative Matrix FactorizationNowadays, non-negative matrix factorization has become popular in face recognition field. Its main idea is decomposing a large matrix into two small matrices, which makes the two small matrices of the decomposed ones do not contain negative. This conforms to the real world of the real data. But NMF does not consider the nearest neighbor relationship in the graph. So we propose Nuclear Norm based Graph Regularization Non-negative matrix factorization (NGNMF), NGNMF uses the nuclear norm minimum of the reconstruction error as criterion, and the alternating direction method of multipliers to calculate the decompositional factors. Compared with the existing method for non-negative matrix factorization (NMF), the proposed NGNMF is more robust for alleviating the effect of illumination and more powerful for eliminating the structural error caused by occlusion. NGNMF is tested using the Yale and the AR face databases. The experimental results show NGNMF is more effective than the current NMF-like method with Frobenius-norm.3、Nuclear Norm based Two-dimensional Supervised Discriminate ProjectionIn order to improve traditional two-dimensional feature extractor robustness to the noise, we present a new method called nuclear norm based two-dimensional Supervised Discriminate Projection (N2DSDP). Unlike traditional supervised subspace algorithm, motivated by maximum scatter difference discriminant criterion, N2DSDP uses nuclear norm redefine the between-class reconstruction error criterion, and then uses 2DLPP construct the affinity graph with the samples from the class. We try to find a group of projection vectors which can minimize the objective function. Experimental results on the AR, YALE, ORL face databases demonstrate the effectiveness of N2DSDP, as compared with related feature extraction methods.4、Exponential Discriminate Locality Preserving Projection AnalysisTo solve the small sample problem of discriminant locality preserving projections, this paper proposes Exponential Discriminate Locality Preserving Projection Analysis (EDLPPA) algorithm for face recognition.This algorithm maps locality preserving within-class and between-class scatters into a new space.In this space both locality preserving within-class and between-class scatters are non-singular, so we can obtain more discriminant information. In the new space, the margin of between-class scatter becomes larger which can improve classification accuracy. The experiments on ORL, FERET and YALE face image database illustrate that the performances of EDLPP outperform LPP and DLPP face recognition algorithms and it also shows the effectiveness of the proposed algorithm.