Regularized discriminant analysis for the small sample size problem in face recognition

It is well-known that the applicability of both linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) to high-dimensional pattern classification tasks such as face recognition (FR) often suffers from the so-called “small sample size” (SSS) problem arising from the small number of available training samples compared to the dimensionality of the sample space. In this paper, we propose a new QDA like method that effectively addresses the SSS problem using a regularization technique. Extensive experimentation performed on the FERET database indicates that the proposed methodology outperforms traditional methods such as Eigenfaces, direct QDA and direct LDA in a number of SSS setting scenarios.     

Inverse Fisher discriminate criteria for small sample size problem and its application to face recognition

This paper addresses the small sample size problem in linear discriminant analysis, which occurs in face recognition applications. Belhumeur et al. [IEEE Trans. Pattern Anal. Mach. Intell. 19 (7) (1997) 711-720] proposed the FisherFace method. We find out that the FisherFace method might fail since after the PCA transform the corresponding within class covariance matrix can still be singular, this phenomenon is verified with the Yale face database. Hence we propose to use an inverse Fisher criteria. Our method works when the number of training images per class is one. Experiment results suggest that this new approach performs well.     

Improving implementation of linear discriminant analysis for the high dimension/small sample size problem

Classification based on Fisher's linear discriminant analysis (FLDA) is challenging when the number of variables largely exceeds the number of given samples. The original FLDA needs to be carefully modified and with high dimensionality implementation issues like reduction of storage costs are of crucial importance. Methods are reviewed for the high dimension/small sample size problem and the one closest, in some sense, to the classical regular approach is chosen. The implementation of this method with regard to computational and storage costs and numerical stability is improved. This is achieved through combining a variety of known and new implementation strategies. Experiments demonstrate the superiority, with respect to both overall costs and classification rates, of the resulting algorithm compared with other methods.     

An efficient algorithm to solve the small sample size problem for LDA

In this paper, we present an efficient algorithm to solve the most discriminant vectors of LDA for high-dimensional data set. The experiments on ORL face database confirm the effectiveness of the proposed method.     

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

We present a modular linear discriminant analysis (LDA) approach for face recognition. A set of observers is trained independently on different regions of frontal faces and each observer projects face images to a lower-dimensional subspace. These lower-dimensional subspaces are computed using LDA methods, including a new algorithm that we refer to as direct, weighted LDA or DW-LDA. DW-LDA combines the advantages of two recent LDA enhancements, namely direct LDA (D-LDA) and weighted pairwise Fisher criteria. Each observer performs recognition independently and the results are combined using a simple sum-rule. Experiments compare the proposed approach to other face recognition methods that employ linear dimensionality reduction. These experiments demonstrate that the modular LDA method performs significantly better than other linear subspace methods. The results also show that D-LDA does not necessarily perform better than the well-known principal component analysis followed by LDA approach. This is an important and significant counterpoint to previously published experiments that used smaller databases. Our experiments also indicate that the new DW-LDA algorithm is an improvement over D-LDA.     

Enhanced semi-supervised local Fisher discriminant analysis for face recognition

An improved manifold learning method, called enhanced semi-supervised local Fisher discriminant analysis (ESELF), for face recognition is proposed. Motivated by the fact that statistically uncorrelated and parameter-free are two desirable and promising characteristics for dimension reduction, a new difference-based optimization objective function with unlabeled samples has been designed. The proposed method preserves the manifold structure of labeled and unlabeled samples in addition to separating labeled samples in different classes from each other. The semi-supervised method has an analytic form of the globally optimal solution and it can be computed based on eigen decomposition. Experiments on synthetic data and AT&T, Yale and CMU PIE face databases are performed to test and evaluate the proposed algorithm. The experimental results and comparisons demonstrate the effectiveness of the proposed method.     

Face recognition using a kernel fractional-step discriminant analysis algorithm

Feature extraction is among the most important problems in face recognition systems. In this paper, we propose an enhanced kernel discriminant analysis (KDA) algorithm called kernel fractional-step discriminant analysis (KFDA) for nonlinear feature extraction and dimensionality reduction. Not only can this new algorithm, like other kernel methods, deal with nonlinearity required for many face recognition tasks, it can also outperform traditional KDA algorithms in resisting the adverse effects due to outlier classes. Moreover, to further strengthen the overall performance of KDA algorithms for face recognition, we propose two new kernel functions: cosine fractional-power polynomial kernel and non-normal Gaussian RBF kernel. We perform extensive comparative studies based on the YaleB and FERET face databases. Experimental results show that our KFDA algorithm outperforms traditional kernel principal component analysis (KPCA) and KDA algorithms. Moreover, further improvement can be obtained when the two new kernel functions are used.     

Adaptively weighted sub-directional two-dimensional linear discriminant analysis for face recognition

A novel image classification algorithm named Adaptively Weighted Sub-directional Two-Dimensional Linear Discriminant Analysis (AWS2DLDA) is proposed in this paper. AWS2DLDA can extract the directional features of images in the frequency domain, and it is applied to face recognition. Some experiments are conducted to demonstrate the effectiveness of the proposed method. Experimental results confirm that the recognition rate of the proposed system is higher than the other popular algorithms.     

A complete fuzzy discriminant analysis approach for face recognition

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.     

An efficient discriminant-based solution for small sample size problem

Classification of high-dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size problem. To address the problem of high-dimensional data classification in the face of a limited number of samples, a novel principal component analysis (PCA) based feature extraction/classification scheme is proposed. The proposed method yields a piecewise linear feature subspace and is particularly well-suited to difficult recognition problems where achievable classification rates are intrinsically low. Such problems are often encountered in cases where classes are highly overlapped, or in cases where a prominent curvature in data renders a projection onto a single linear subspace inadequate. The proposed feature extraction/classification method uses class-dependent PCA in conjunction with linear discriminant feature extraction and performs well on a variety of real-world datasets, ranging from digit recognition to classification of high-dimensional bioinformatics and brain imaging data.     

Kernel discriminant transformation for image set-based face recognition

This study presents a novel kernel discriminant transformation (KDT) algorithm for face recognition based on image sets. As each image set is represented by a kernel subspace, we formulate a KDT matrix that maximizes the similarities of within-kernel subspaces, and simultaneously minimizes those of between-kernel subspaces. Although the KDT matrix cannot be computed explicitly in a high-dimensional feature space, we propose an iterative kernel discriminant transformation algorithm to solve the matrix in an implicit way. Another perspective of similarity measure, namely canonical difference, is also addressed for matching each pair of the kernel subspaces, and employed to simplify the formulation. The proposed face recognition system is demonstrated to outperform existing still-image-based as well as image set-based face recognition methods using the Yale Face database B, Labeled Faces in the Wild and a self-compiled database.     

Generalized re-weighting local sampling mean discriminant analysis

Despite the general success in the pattern recognition community, linear discriminant analysis (LDA) has four intrinsic drawbacks. In this paper, we propose a new feature extraction algorithm, namely, local sampling mean discriminant analysis (LSMDA), to make up for the first three drawbacks, and a generalized re-weighting (GRW) framework to make up for the fourth drawback. Extensive experiments are conducted on both synthetic and real-world datasets to evaluate the classification performance of our work. The experimental results demonstrate the effectiveness of both LSMDA and the GRW framework in classifications.     

A novel adaptive crossover bacterial foraging optimization algorithm for linear discriminant analysis based face recognition

This paper presents a modified bacterial foraging optimization algorithm called adaptive crossover bacterial foraging optimization algorithm (ACBFOA), which incorporates adaptive chemotaxis and also inherits the crossover mechanism of genetic algorithm. First part of the research work aims at improvising evaluation of the optimal objective function values. The idea of using adaptive chemotaxis is to make it computationally efficient and crossover technique is to search nearby locations by offspring bacteria. Four different benchmark functions are considered for performance evaluation. The purpose of this research work is also to investigate a face recognition algorithm with improved recognition rate. In this connection, we propose a new algorithm called ACBFO-Fisher. The proposed ACBFOA is used for finding optimal principal components for dimension reduction in linear discriminant analysis (LDA) based face recognition. Three well-known face databases, FERET, YALE and UMIST, are considered for validation. A comparison with the results of earlier methods is presented to reveal the effectiveness of the proposed ACBFO-Fisher algorithm.     

Multiclass classifiers based on dimension reduction with generalized LDA

Linear discriminant analysis (LDA) has been widely used for dimension reduction of data sets with multiple classes. The LDA has been recently extended to various generalized LDA methods that are applicable regardless of the relative sizes between the data dimension and the number of data items. In this paper, we propose several multiclass classifiers based on generalized LDA (GLDA) algorithms, taking advantage of the dimension reducing transformation matrix without requiring additional training or parameter optimization. A marginal linear discriminant classifier (MLDC), a Bayesian linear discriminant classifier (BLDC), and a one-dimensional BLDC are introduced for multiclass classification. Our experimental results illustrate that these classifiers produce higher ten-fold cross validation accuracy than kNN and centroid-based classifiers in the reduced dimensional space obtained from GLDA.     

Two-dimensional discriminant transform for face recognition

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.     

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

In this paper, we present a new approach for fingerprint classification based on discrete Fourier transform (DFT) and nonlinear discriminant analysis. Utilizing the DFT and directional filters, a reliable and efficient directional image is constructed from each fingerprint image, and then nonlinear discriminant analysis is applied to the constructed directional images, reducing the dimension dramatically and extracting the discriminant features. The proposed method explores the capability of DFT and directional filtering in dealing with low-quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification. Experimental results demonstrates competitive performance compared with other published results.     

Regularized discriminant analysis for face recognition

This paper studies regularized discriminant analysis (RDA) in the context of face recognition. We check RDA sensitivity to different photometric preprocessing methods and compare its performance to other classifiers. Our study shows that RDA is better able to extract the relevant discriminatory information from training data than the other classifiers tested, thus obtaining a lower error rate. Moreover, RDA is robust under various lighting conditions while the other classifiers perform badly when no photometric method is applied.     

Emulating biological strategies for uncontrolled face recognition

Face recognition technology is of great significance for applications involving national security and crime prevention. Despite enormous progress in this field, machine-based system is still far from the goal of matching the versatility and reliability of human face recognition. In this paper, we show that a simple system designed by emulating biological strategies of human visual system can largely surpass the state-of-the-art performance on uncontrolled face recognition. In particular, the proposed system integrates dual retinal texture and color features for face representation, an incremental robust discriminant model for high level face coding, and a hierarchical cue-fusion method for similarity qualification. We demonstrate the strength of the system on the large-scale face verification task following the evaluation protocol of the Face Recognition Grand Challenge (FRGC) version 2 Experiment 4. The results are surprisingly well: Its modules significantly outperform their state-of-the-art counterparts, such as Gabor image representation, local binary patterns, and enhanced Fisher linear discriminant model. Furthermore, applying the integrated system to the FRGC version 2 Experiment 4, the verification rate at the false acceptance rate of 0.1 percent reaches to 93.12 percent.     

(2D)LDA: An efficient approach for face recognition

Although 2DLDA algorithm obtains higher recognition accuracy, a vital unresolved problem of 2DLDA is that it needs huge feature matrix for the task of face recognition. To overcome this problem, this paper presents an efficient approach for face image feature extraction, namely, (2D)²LDA method. Experimental results on ORL and Yale database show that the proposed method obtains good recognition accuracy despite having less number of coefficients.     

Complete discriminant evaluation and feature extraction in kernel space for face recognition

This work proposes a method to decompose the kernel within-class eigenspace into two subspaces: a reliable subspace spanned mainly by the facial variation and an unreliable subspace due to limited number of training samples. A weighting function is proposed to circumvent undue scaling of eigenvectors corresponding to the unreliable small and zero eigenvalues. Eigenfeatures are then extracted by the discriminant evaluation in the whole kernel space. These efforts facilitate a discriminative and stable low-dimensional feature representation of the face image. Experimental results on FERET, ORL and GT databases show that our approach consistently outperforms other kernel based face recognition methods.