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In this paper, we propose a two-phase test sample representation method for face recognition. The first phase of the proposed method seeks to represent the test sample as a linear combination of all the training samples and exploits the representation ability of each training sample to determine M “nearest neighbors” for the test sample. The second phase represents the test sample as a linear combination of the determined M nearest neighbors and uses the representation result to perform classification. We propose this method with the following assumption: the test sample and its some neighbors are probably from the same class. Thus, we use the first phase to detect the training samples that are far from the test sample and assume that these samples have no effects on the ultimate classification decision. This is helpful to accurately classify the test sample. We will also show the probability explanation of the proposed method. A number of face recognition experiments show that our method performs very well. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, some studies have been made on the essence of fuzzy linear discriminant analysis (F-LDA) algorithm and fuzzy support vector machine (FSVM) classifier, respectively. As a kernel-based learning machine, FSVM is represented with the fuzzy membership function while realizing the same classification results with that of the conventional pair-wise classification. It outperforms other learning machines especially when unclassifiable regions still remain in those conventional classifiers. However, a serious drawback of FSVM is that the computation requirement increases rapidly with the increase of the number of classes and training sample size. To address this problem, an improved FSVM method that combines the advantages of FSVM and decision tree, called DT-FSVM, is proposed firstly. Furthermore, in the process of feature extraction, a reformative F-LDA algorithm based on the fuzzy k-nearest neighbors (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership grade, which is incorporated into the redefinition of the scatter matrices. In particular, considering the fact that the outlier samples in the patterns may have some adverse influence on the classification result, we developed a novel F-LDA algorithm using a relaxed normalized condition in the definition of fuzzy membership function. Thus, the classification limitation from the outlier samples is effectively alleviated. Finally, by making full use of the fuzzy set theory, a complete F-LDA (CF-LDA) framework is developed by combining the reformative F-LDA (RF-LDA) feature extraction method and DT-FSVM classifier. This hybrid fuzzy algorithm is applied to the face recognition problem, extensive experimental studies conducted on the ORL and NUST603 face images databases demonstrate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

This paper examines the theory of kernel Fisher discriminant analysis (KFD) in a Hilbert space and develops a two-phase KFD framework, i.e., kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). This framework provides novel insights into the nature of KFD. Based on this framework, the authors propose a complete kernel Fisher discriminant analysis (CKFD) algorithm. CKFD can be used to carry out discriminant analysis in "double discriminant subspaces." The fact that; it can make full use of two kinds of discriminant information, regular arid irregular, makes CKFD a more powerful discriminator. The proposed algorithm was tested and evaluated using the FERET face database and the CENPARMI handwritten numeral database. The experimental results show that CKFD outperforms other KFD algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a Complex LDA based combined Fisherfaces framework, coined Complex Fisherfaces, is developed for face feature extraction and recognition. In this framework, Principal Component Analysis (PCA) and Kernel PCA (KPCA) are first used for feature extraction. Then, the resulting PCA-based linear features and KPCA-based nonlinear features are integrated by complex vectors and, Complex LDA is further employed for feature fusion. The proposed method is tested on a subset of FERET database. The experimental results demonstrate that Complex Fisherfaces outperforms Fisherfaces and Kernel Fisherfaces. Also, the complex vector based parallel feature fusion strategy is demonstrated to be much more effective and robust than the super-vector based serial feature fusion strategy for face recognition. [Copyright &y& Elsevier]

A new strategy of parallel feature fusion is introduced in this paper. A complex vector is first used to represent the parallel combined features. Then, the traditional linear projection analysis methods, including principal component analysis, K–L expansion and linear discriminant analysis, are generalized for feature extraction in the complex feature space. Finally, the developed parallel feature fusion methods are tested on CENPARMI handwritten numeral database, NUST603 handwritten Chinese character database and ORL face image database. The experimental results indicate that the classification accuracy is increased significantly under parallel feature fusion and also demonstrate that the developed parallel fusion is more effective than the classical serial feature fusion. [Copyright &y& Elsevier]

PCA plus LDA is a popular framework for linear discriminant analysis (LDA) in high dimensional and singular case. In this paper, we focus on building a theoretical foundation for this framework. Moreover, we point out the weakness of the previous LDA based methods, and suggest a complete PCA plus LDA algorithm. Experimental results on ORL face image database indicate that the proposed method is more effective than the previous ones. [Copyright &y& Elsevier]

In this paper we view the optimal set of discriminant vectors as a global transform, and consider its separability from a global view point. Based on this idea, the concept of a generalised Fisher discriminant criterion and that of a generalised optimal set of discriminant vectors is introduced. After that, a new algorithm is given to calculate the generalised optimal set of discriminant vectors defined in this paper, which is particularly suited to the case of a small number of samples where the scatter matrix is singular. It is then applied to an experiment on human facial recognition, and the results show that the new algorithm is superior to existing methods in terms of correct classification rate. [ABSTRACT FROM AUTHOR]

Abstract: Human faces display different color and recent research efforts show that color is useful for face recognition. This paper presents a discriminant color space method and demonstrates its effectiveness using the FRGC Experiment 4 database and the AR database. We find that the discriminant color space is an approximate double-zero-sum (DZS) color space, and further show that a color space with DZS characteristic is more powerful than other color spaces without this characteristic. We finally provide the justification for why the DZS color spaces is more effective than non-DZS color spaces for face verification and recognition from the mutual correlation point of view. [Copyright &y& Elsevier]

Abstract: The discriminative common vectors (DCV) algorithm is a recently addressed discriminant method, which shows better face recognition effects than some commonly used linear discriminant algorithms. The radial basis function (RBF) neural network is widely applied to the function approximation and pattern classification. One of the interesting research topics of RBF network is how to set appropriate hidden-layer units. Based on DCV, we design a new nonlinear feature extraction algorithm that is the kernel DCV (KDCV) algorithm and we employ the DCV generated by KDCV as the hidden-layer units of the RBF network. Then we present a novel face recognition approach that is the KDCV-RBF approach. Testing on a public large face database (AR database), the experimental results demonstrate that KDCV-RBF is an effective face recognition approach, which outperforms several representative recognition methods. [Copyright &y& Elsevier]

Abstract: A study has been made on an extreme case of generalized optimal set of discriminant vectors. Equivalence between the generalized K–L transformation and the generalized optimal discriminant transformation is proved under the condition that the population scatter matrix of training samples is nonsingular. A new algorithm for determining the generalized optimal set of discriminant vectors is proposed based on the above theory, which is applied to the feature extraction of human face images. The results of experiments conducted on ORL and Yale databases show the effectiveness of the new feature extraction algorithm based on the extreme case of the generalized optimal discriminant transformation. [Copyright &y& Elsevier]

Abstract: In this paper, a reformative kernel Fisher discriminant (KFD) algorithm with fuzzy set theory is studied. The KFD algorithm is effective to extract nonlinear discriminative features of input samples using the kernel trick. However, the conventional KFD algorithm assumes the same level of relevance of each sample to the corresponding class. In this paper, a fuzzy kernel Fisher discriminant (FKFD) algorithm is proposed. Distribution information of samples is represented with fuzzy membership degree and this information is utilized to redefine corresponding scatter matrices which are different to the conventional KFD algorithm and effective to extract discriminative features from overlapping (outlier) samples. Experimental results on the ORL face database demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper develops a method called locally principal component analysis (LPCA) for data representation. LPCA is a linear and unsupervised subspace-learning technique, which focuses on the data points within local neighborhoods and seeks to discover the local structure of data. This local structure may contain useful information for discrimination. LPCA is tested and evaluated using the AT&T face database. The experimental results show that LPCA is effective for dimension reduction and more powerful than PCA for face recognition. [Copyright &y& Elsevier]

Kernel-based methods have been of wide concern in the field of machine learning and neurocomputing. In this paper, a new Kernel Fisher discriminant analysis (KFD) algorithm, called complete KFD (CKFD), is developed. CKFD has two advantages over the existing KFD algorithms. First, its implementation is divided into two phases, i.e., Kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (FLD), which makes it more transparent and simpler. Second, CKFD can make use of two categories of discriminant information, which makes it more powerful. The proposed algorithm was applied to face recognition and tested on a subset of the FERET database. The experimental results demonstrate that CKFD is significantly better than the algorithms of Kernel Fisherface and Kernel Eigenface. [Copyright &y& Elsevier]

This paper proposes a novel and real-time classifiers combination approach, group decision-making combination (GDC) approach, which can dynamically select the classifiers and perform linear combination. We also prove that the orthogonal wavelet transform can be regarded as an effective image''s preprocessing tool adapted to classifiers combination. GDC has been successfully used for face recognition, which can improve on the recognition rate for the algebraic features. Experiment results also show that it is superior to the conventional combination method, majority voting method. [Copyright &y& Elsevier]

Abstract: Manifold learning is an effective dimensional reduction technique for face feature extraction, which, generally speaking, tends to preserve the local neighborhood structures of given samples. However, neighbors of a sample often comprise more inter-class data than intra-class data, which is an undesirable effect for classification. In this paper, we address this problem by proposing a subclass-center based manifold preserving projection (SMPP) approach, which aims at preserving the local neighborhood structure of subclass-centers instead of given samples. We theoretically show from a probability perspective that, neighbors of a subclass-center would comprise of more intra-class data than inter-class data, and thus is more desirable for classification. In order to take full advantage of the class separability, we further propose the discriminant SMPP (DSMPP) approach, which incorporates the subclass discriminant analysis (SDA) technique to SMPP. In contrast to related discriminant manifold learning methods, DSMPP is formulated as a dual-objective optimization problem and we present analytical solution to it. Experimental results on the public AR, FERET and CAS-PEAL face databases demonstrate that the proposed approaches are more effective than related manifold learning and discriminant manifold learning methods in classification performance. [Copyright &y& Elsevier]

When the conventional interest operator is used as the feature extraction procedure of face recognition, it has the following two shortcomings: first, though the purpose of the conventional interest operator is to use the intensity variation between neighboring pixels to represent the image, it cannot obtain all variation information between neighboring pixels. Second, under varying lighting conditions two images of the same face usually have different feature extraction results even though the face itself does not have obvious change. In this paper, we propose two new interest operators for face recognition, which are used to calculate the pixel intensity variation information of overlapping blocks produced from the original face image. The following two factors allow the new operators to perform better than the conventional interest operator: the first factor is that by taking the relative rather than absolute variation of the pixel intensity as the feature of an image block, the new operators can obtain robust block features. The second factor is that the scheme to partition an image into overlapping rather than non-overlapping blocks allows the proposed operators to produce more representation information for the face image. Experimental results show that the proposed operators offer significant accuracy improvement over the conventional interest operator. [Copyright &y& Elsevier]

Abstract: This paper formulates maximum scatter difference (MSD) criterion in the kernel-including feature space and develops a two-phase kernel maximum scatter difference criterion: KPCA plus MSD. The proposed method first maps the input data into a potentially much higher dimensional feature space by virtue of nonlinear kernel trick, and in such a way, the problem of feature extraction in the nonlinear space is overcome. Then the scatter difference between between-class and within-class as discriminant criterion is defined on the basis of the above computation; therefore, the singularity problem of the within-class scatter matrix due to small sample size problem occurred in classical Fisher discriminant analysis is avoided. The results of experiments conducted on a subset of FERET database, Yale database indicate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: By formulating two-dimensional principle component analysis (2DPCA) as a mathematical form different from the conventional 2DPCA, we present theoretical basis of 2DPCA and show the theoretical similarities and differences between 2DPCA and PCA. We also show that 2DPCA owns its decorrelation property and the feature vectors extracted from matrices are uncorrelated. We use the proposed mathematical form to show that 2DPCA is the best approach for directly extract features from matrices. We also present in detail 2DPCA Schemes 1 and 2, two schemes to implement the proposed mathematical form. The two schemes transform original images into different spaces, respectively, 2DPCA Scheme 1 enhances the transverse characters of images, whereas the second scheme enhances vertical characters of images. We propose a feature fusion approach for achieving better recognition results by combining the features generated from the two schemes of 2DPCA. The proposed fusion approach is tested on face recognition tasks and is found to be more accurate than both 2DPCA Scheme 1 and 2DPCA Scheme 2. [Copyright &y& Elsevier]

Abstract: Nonlinear discriminant analysis may be transformed into the form of kernel-based discriminant analysis. Thus, the corresponding discriminant direction can be solved by linear equations. From the view of feature space, the nonlinear discriminant analysis is still a linear method, and it is provable that in feature space the method is equivalent to Fisher discriminant analysis. We consider that one linear combination of parts of training samples, called “significant nodes”, can replace the total training samples to express the corresponding discriminant vector in feature space to some extent. In this paper, an efficient algorithm is proposed to determine “significant nodes” one by one. The principle of determining “significant nodes” is simple and reasonable, and the consequent algorithm can be carried out with acceptable computation cost. Depending on the kernel functions between test samples and all “significant nodes”, classification can be implemented. The proposed method is called fast kernel-based nonlinear method (FKNM). It is noticeable that the number of “significant nodes” may be much smaller than that of the total training samples. As a result, for two-class classification problems, the FKNM will be much more efficient than the naive kernel-based nonlinear method (NKNM). The FKNM can be also applied to multi-class via two approaches: one-against-the-rest and one-against-one. Although there is a view that one-against-one is superior to one-against-the-rest in classification efficiency, it seems that for the FKNM one-against-the-rest is more efficient than one-against-one. Experiments on benchmark and real datasets illustrate that, for two-class and multi-class classifications, the FKNM is effective, feasible and much efficient. [Copyright &y& Elsevier]

Abstract: This paper formulates independent component analysis (ICA) in the kernel-inducing feature space and develops a two-phase kernel ICA algorithm: whitened kernel principal component analysis (KPCA) plus ICA. KPCA spheres data and makes the data structure become as linearly separable as possible by virtue of an implicit nonlinear mapping determined by kernel. ICA seeks the projection directions in the KPCA whitened space, making the distribution of the projected data as non-gaussian as possible. The experiment using a subset of FERET database indicates that the proposed kernel ICA method significantly outperform ICA, PCA and KPCA in terms of the total recognition rate. [Copyright &y& Elsevier]

Abstract: This paper develops a new image feature extraction and recognition method coined two-dimensional linear discriminant analysis (2DLDA). 2DLDA provides a sequentially optimal image compression mechanism, making the discriminant information compact into the up-left corner of the image. Also, 2DLDA suggests a feature selection strategy to select the most discriminative features from the corner. 2DLDA is tested and evaluated using the AT&T face database. The experimental results show 2DLDA is more effective and computationally more efficient than the current LDA algorithms for face feature extraction and recognition. [Copyright &y& Elsevier]