ORL Face Image Research Articles

Fuzzy local maximal marginal embedding for feature extraction

In graph-based linear dimensionality reduction algorithms, it is crucial to construct a neighbor graph that can correctly reflect the relationship between samples. This paper presents an improved algorithm called fuzzy local maximal marginal embedding (FLMME) for linear dimensionality reduction. Significantly differing from the existing graph-based algorithms is that two novel fuzzy gradual graphs are constructed in FLMME, which help to pull the near neighbor samples in same class nearer and nearer and repel the far neighbor samples of margin between different classes farther and farther when they are projected to feature subspace. Through the fuzzy gradual graphs, FLMME algorithm has lower sensitivities to the sample variations caused by varying illumination, expression, viewing conditions and shapes. The proposed FLMME algorithm is evaluated through experiments by using the WINE database, the Yale and ORL face image databases and the USPS handwriting digital databases. The results show that the FLMME outperforms PCA, LDA, LPP and local maximal marginal embedding.

Maximal local interclass embedding with application to face recognition

Dimensionality reduction of high dimensional data is involved in many problems in information processing. A new dimensionality reduction approach called maximal local interclass embedding (MLIE) is developed in this paper. MLIE can be viewed as a linear approach of a multimanifolds-based learning framework, in which the information of neighborhood is integrated with the local interclass relationships. In MLIE, the local interclass graph and the intrinsic graph are constructed to find a set of projections that maximize the local interclass scatter and the local intraclass compactness simultaneously. This characteristic makes MLIE more powerful than marginal Fisher analysis (MFA). MLIE maintains all the advantages of MFA. Moreover, the computational complexity of MLIE is less than that of MFA. The proposed algorithm is applied to face recognition. Experiments have been performed on the Yale, AR and ORL face image databases. The experimental results show that owing to the locally discriminating property, MLIE consistently outperforms up-to-date MFA, Smooth MFA, neighborhood preserving embedding and locality preserving projection in face recognition.

An optimal symmetrical null space criterion of Fisher discriminant for feature extraction and recognition

Linear discriminant analysis (LDA) is one of the most effective feature extraction methods in statistical pattern recognition, which extracts the discriminant features by maximizing the so-called Fisher’s criterion that is defined as the ratio of between-class scatter matrix to within-class scatter matrix. However, classification of high-dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size (SSS) problem. A popular approach to the SSS problem is the removal of non-informative features via subspace-based decomposition techniques. Motivated by this viewpoint, many elaborate subspace decomposition methods including Fisherface, direct LDA (D-LDA), complete PCA plus LDA (C-LDA), random discriminant analysis (RDA) and multilinear discriminant analysis (MDA), etc., have been developed, especially in the context of face recognition. Nevertheless, how to search a set of complete optimal subspaces for discriminant analysis is still a hot topic of research in area of LDA. In this paper, we propose a novel discriminant criterion, called optimal symmetrical null space (OSNS) criterion that can be used to compute the Fisher’s maximal discriminant criterion combined with the minimal one. Meanwhile, by the reformed criterion, the complete symmetrical subspaces based on the within-class and between-class scatter matrices are constructed, respectively. Different from the traditional subspace learning criterion that derives only one principal subspace, in our approach two null subspaces and their orthogonal complements were all obtained through the optimization of OSNS criterion. Therefore, the algorithm based on OSNS has the potential to outperform the traditional LDA algorithms, especially in the cases of small sample size. Experimental results conducted on the ORL, FERET, XM2VTS and NUST603 face image databases demonstrate the effectiveness of the proposed method.

Locality preserving discriminant projections for face and palmprint recognition

A new subspace learning algorithm called locality preserving discriminant projections (LPDP) is proposed by adding the criterion of maximum margin criterion (MMC) into the objective function of locality preserving projections (LPP). LPDP retains the locality preserving characteristic of LPP and utilizes the global discriminative structures obtained from MMC, which can maximize the between-class distance and minimize the within-class distance. Thus, our proposed LPDP combining manifold criterion and Fisher criterion has more discriminanting power, and is more suitable for recognition tasks than LPP, which considers only the local information for classification tasks. Moreover, two kinds of tensorized (multilinear) forms of LPDP are also derived in this paper. One is iterative while the other is non-iterative. The proposed LPDP method is applied to face and palmprint biometrics and is examined using the Yale and ORL face image databases, as well as the PolyU palmprint database. Experimental results demonstrate the effectiveness of the proposed LPDP method.

Quotient vs. difference: Comparison between the two discriminant criteria

Two discriminant criteria—quotient and difference, are commonly used in linear discriminant analysis. In the paper, we experiment with the CENPARMI handwritten numeral database, the NUST603 handwritten Chinese character database, the ORL face image database and the FERET face image database and find that the quotient criterion is better than the difference criterion for large sample size problems such as the character recognition, while the difference criterion is better for small sample size problems such as face recognition. Through theoretical analysis, the defect of the difference criterion—the correlation among discriminant vectors is revealed, and it is testified that the quotient criterion is superior to the difference criterion in general, if the instability of denominator can be overcome. Otherwise, the difference criterion might be better. Finally, the two criteria (quotient and difference) are unified into one framework in the paper.

Discriminant analysis approach using fuzzy fourfold subspaces model

In this paper, some studies have been made on the essence of a novel fuzzy discriminant analysis (FDA) on the fourfold-objective model (FOM). First, a fourfold-objective model on the discriminant analysis is developed, by which a set of integrated subspaces derived from within-class and between-class scatter matrices are constructed, respectively. Second, an improved FDA (IFDA) algorithm based on the relaxed normalized condition is proposed to achieve the distribution information of each sample represented with fuzzy membership grade, which is incorporated into the redefinition of Fisher's scatter matrices. Therefore, the presented algorithm has the potential to outperform the traditional subspace learning algorithms, especially in the cases of small sample size. Experimental results conducted on the ORL, NUST603, FERET and Yale face image databases demonstrate the effectiveness of the proposed method.

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.

A generalised K-L expansion method which can deal with small sample size and high-dimensional problems

The K-L expansion method, which is able to extract the discriminatory information contained in class-mean vectors, is generalised, in this paper, to make it suitable for solving small sample size problems. We further investigate, theoretically, how to reduce the method’s computational complexity in high-dimensional cases. As a result, a simple and efficient GKLE algorithm is developed. We test our method on the ORL face image database and the NUST603 handwritten Chinese character database, and our experimental results demonstrate that GKLE outperforms the existing techniques of PCA, PCA plus LDA, and Direct LDA.

Feature fusion: parallel strategy vs. serial strategy

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.

Why can LDA be performed in PCA transformed space?

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.