SUPERVISED REGULARIZATION LOCALITY-PRESERVING PROJECTION METHOD FOR FACE RECOGNITION

When locality preserving projection (LPP) method was originally proposed, it takes as the LPP solution the minimum eigenvalue solution of an eigenequation. After that, LPP has been used for image recognition problems such as face recognition. However, almost no researcher realizes that LPP usually encounters several difficulties when applied to the image recognition problem. For example, since image recognition problems are usually small sample size (SSS) problems, the corresponding eigenequation cannot be directly solved. In addition, it seems that even if one can obtain the solution of the eigenequation by using the numerical analysis approach, the obtained conventional LPP solution might produce the `presentation confusion' problem for samples from different classes, which is disadvantageous for the classification to procedure a high accuracy. In this paper we first thoroughly investigate the characteristics and drawbacks of the conventional LPP solution in the small sample size (SSS) problem in which the sample number is smaller than the data dimension. In order to overcome these drawbacks, we propose a new LPP solution for the SSS problem, which has clear physical meaning and can be directly and easily worked out because it is generated from a non-singular eigenequation. Experimental results the proposed solution scheme can produce a much lower classification error rate than the conventional LPP solution.

LPP solution schemes for use with face recognition

Dimensionality reduction technologies are very important for pattern representation and recognition. Among them, locality preserving projection (LPP) is a manifold dimensionality reduction scheme and has been successfully applied to face recognition. However, LPP is an unsupervised linear approach, its performance will degrade for classification tasks. Especially, when the dimension of input space is greater than the number of training data, singularity problem will occur and LPP cannot be implemented directly. To tackle the draw backs of LPP algorithm, this paper proposes a novel regularized LPP(RLPP) approach using supervised graph and regularization technique. The proposed RLPP method has been tested and evaluated with two public available databases, namely ORL and FERET databases. Experimental results show that the proposed RLPP approach surpasses Laplacianface and Direct-LPP (DLPP) methods.

Face recognition technology has evolved as an enchanting solution to address the contemporary needs in order to perform identification and verification of identity claims. By advancing the feature extraction methods and dimensionality reduction techniques in the application of pattern recognition, a number of face recognition systems has been developed with distinct degrees of success. Locality preserving projection (LPP) is a recently proposed method for unsupervised linear dimensionality reduction. LPP preserve the local structure of face image space which is usually more significant than the global structure preserved by principal component analysis (PCA) and linear discriminant analysis (LDA). This paper focuses on a systematic analysis of locality-preserving projections and the application of LPP in combination with an existing technique This combined approach of LPP through MPCA can preserve the global and the local structure of the face image which is proved very effective. Proposed approach is tested using the AT & T face database. Experimental results show the significant improvements in the face recognition performance in comparison with some previous methods.

Quaternion-based improved LPP method for color face recognition

Enhanced locality preserving projections using robust path based similarity

Due to its wide applications in practice, face recognition has been an active research topic. With the availability of adequate training samples, many machine learning methods could yield high face recognition accuracy. However, under the circumstance of inadequate training samples, especially the extreme case of having only a single training sample, face recognition becomes challenging. How to deal with conflicting concerns of the small sample size and high dimensionality in one-sample face recognition is critical for its achievable recognition accuracy and feasibility in practice. Being different from the conventional methods for global face recognition based on generalization ability promotion and local face recognition depending on image segmentation, a single-sample face recognition algorithm based on locality preserving projection (LPP) feature transfer is proposed here. First, transfer sources are screened to obtain the selective sample source using the whitened cosine similarity metric. Second, we project the vectors of source faces and target faces into feature subspace by LPP, respectively, and calculate the feature transfer matrix to approximate the mapping relationship on source faces and target faces in subspace. Then, the feature transfer matrix is used on training samples to transfer the original macro characteristics to target macro characteristics. Finally, the nearest neighbor classifier is used for face recognition. Our results based on popular databases FERET, ORL, and Yale demonstrate the superiority of the proposed LPP feature transfer-based one-sample face recognition algorithm when compared with popular single-sample face recognition algorithms, such as (PC) $^{2}\text{A}$ and Block FLDA.

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

An appearance-based face recognition approach called the Local Fisher Discriminant Embedding (LFDE) method is proposed in this paper. By using LFDE, the face images are mapped into a face subspace for analysis. Different from Linear Discriminant Analysis (LDA), which effectively sees only the Euclidean structure of face space, LFDE finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure. Different from Locality Preserving Projections (LPP) and Unsupervised Discriminant projections (UDP) which ignore the class label information, LFDE searches for the project axes on which the data points of different classes are far from each other while requiring data points of the same class to be close to each other. We compare the proposed LFDE approach with PCA, FDA, LPP, and UDP on two different face databases. Experimental results suggest that the proposed LFDE approach provides a better representation and achieves higher accuracy in face recognition.

A new image feature extraction method for face recognition called Tri-direction 2D-Fisher Discriminant Analysis (T2D-FDA) is proposed to deal with the Small Sample Size (SSS) problem in conventional 1D-Fisher Discriminant Analysis (1D-FDA). Moreover, the essence of T2D-FDA is investigated, and the equivalence of the left-multiplying 2D-FDA of the original image matrices and the left-multiplying D2D-FDA of diagonal image matrices is verified if each column is viewed as a computational unit. Different from the 1D-LDA based approaches, the T2D-FDA is based on 2D image matrices rather than column vectors, so the image matrix does not need to be transformed into a long vector before feature extraction. The advantage arising in this way is that the SSS problem does not exist anymore because within-class scatter matrices constructed is full-rank in T2D-FDA. The proposed method is applied to face recognition where only few training images exist for each subject. Experiment results show T2D-FDA outperforms the current linear subspace methods in SSS problem on four public databases: ORL, Yale, AR and FERET face databases.

Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance.

In order to search for an efficient feature extraction approach for face recognition,a method based on feature level fusion was presented.This method integrated Locality Preserving Projection(LPP) with Maximum Margin Criterion(MMC).Firstly,LPP was performed on training samples set,so the projection of each training sample on LPP subspace could be got.Further,MMC algorithm was performed on all the obtained projections to get more efficient discriminant features for recognition.Nearest Neighborhood(NN) algorithm was used to construct classifiers.The experiments on the ORL face database show that the recognition rate of the proposed method is high when pose,illumination condition,face expression and training sample number change.

In the present work, appearance-based face recognition method called the Laplacianface approach is used. The face images are mapped into a face subspace for analysis by using Locality Preserving Projections(LPP). The technique is different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) which effectively see only the Euclidean structure of face space. The main goal of LPP is to preserve neighbourhood structure of the data set optimally and hence obtain a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the Eigen functions of the Laplace Beltrami operator on the face manifold. Hence, by using this approach undesired variations because of facial expression, changes in lighting conditions, and pose may be eliminated or reduced. Performance analysis of face recognition is carried out on standard databases using both LPP technique and PCA technique. For comparison purpose, PCA with ANN classifier based on Back Propagation Feed Forward Neural Network is also developed and being used for training the input face images and then testing. LPP approach outperforms PCA with ANN, and provides better face representation and also achieves lower error rate.

Linear Discriminant Analysis (LDA) has been one of the popular subspace methods for face recognition. But this method suffers from the small sample size (SSS) problem, also known as 'curse of dimensionality'. Various techniques have been proposed in literature to overcome this limitation. But it is still unclear which method provides the best solution to SSS problem. In this paper, we have investigated the performance of some popular subspace methods such as principal component analysis (PCA), PCA + LDA, LDA via QR decomposition, Null-space LDA, Exponential Discriminant Analysis (EDA), PCA+EDA etc. Extensive experiments have been performed on five publically available face datasets viz. AR, CMU-PIE, PIX, Yale and YaleB. The performance is measured in terms of average classification accuracy. Experimental results show that the performance increases with the increase in the number of images per person in training set irrespective of the datasets. There is no clear winner among the subspace methods under investigation. But, the performance of PCA+LDA and PCA+EDA is consistent in tackling SSS problem irrespective of the dataset and can also handle the illumination variation in face recognition.

We made two contributions in this paper. First, a new method called two-dimensional fisher discriminant analysis (2D-FDA) is proposed to deal with the small sample size (SSS) problem in LDA based face recognition. Second, appearance and depth information are combined to improve face recognition rate. Different from the conventional 1D-FDA (PCA plus LDA) approaches, 2D-FDA is based on 2D image matrices rather than column vectors so the image matrix does not need to be transformed into a long vector before feature extraction. The advantage arising in this way is that the SSS problem does not exist any more because the between-class and within-class scatter matrices constructed in 2D-FDA are both of full-rank. 2D FDA and 1D FDA (PCA plus LDA) are evaluated respectively with a problem that combines appearance and depth information for face recognition. We investigate the complete range of linear combinations to reveal the interplay between these two paradigms. The recognition rate by the combination is better than either appearance alone or depth alone. It is verified that 2D-FDA outperforms 1D FDA