Tri-Direction 2D-Fisher Discriminant Analysis (T2D-FDA) for Feature Extraction

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

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.

In this paper, a novel image discriminant analysis method, coined two-dimensional discriminant transform based on scatter difference criterion (2DSDD), is developed for image representation. The proposed 2DSDD scheme adopts the difference of both between-class scatter and within-class scatter as discriminant criterion. In this way, the small sample size problem usually occurred in the traditional Fisher discriminant analysis (LDA) is essentially avoided. In addition, the developed method directly depends on image matrices. That is to say, it is not necessary to convert the image matrix into high-dimensional image vector like those conventional linear discriminant methods prior to feature extraction so that much computational time would be saved. Finally, the experimental results on the ORL face database indicate that the proposed method outperforms Fisherfaces, the standard scatter difference discriminant analysis, not only in the computation efficiency, but also in its recognition performance.

The small sample size (SSS) problem is one of the major problems encountered when traditional kernel discriminant analysis methods are applied to high-dimensional pattern recognition tasks. Different methods have been proposed to solve this problem. In this paper, we introduce a new kernel discriminant analysis algorithm, which is able to effectively address the SSS problem and extract a set of optimal discriminant vectors without any lose of useful discriminant information. Experiments performed on radar target recognition using range profiles indicate that the proposed method outperforms some existing kernel discriminant algorithms, such as generalized discriminant analysis and kernel direct discriminant analysis, in terms of recognition rate.

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.

Most finger vein authentication systems suffer from the problem of small sample size. However, the data augmentation can alleviate this problem to a certain extent but did not fundamentally solve the problem of category diversity. So the researchers resort to pre-training or multi-source data joint training methods, but these methods will lead to the problem of user privacy leakage. In view of the above issues, this paper proposes a federated learning-based finger vein authentication framework (FedFV) to solve the problem of small sample size and category diversity while protecting user privacy. Through training under FedFV, each client can share the knowledge learned from its user’s finger vein data with the federated client without causing template leaks. In addition, we further propose an efficient personalized federated aggregation algorithm, named federated weighted proportion reduction (FedWPR), to tackle the problem of non-independent identically distribution caused by client diversity, thus achieving the best performance for each client. To thoroughly evaluate the effectiveness of FedFV, comprehensive experiments are conducted on nine publicly available finger vein datasets. Experimental results show that FedFV can improve the performance of the finger vein authentication system without directly using other client data. To the best of our knowledge, FedFV is the first personalized federated finger vein authentication framework, which has some reference value for subsequent biometric privacy protection research.

This chapter shows the solutions of LDA for small sample-size (SSS) problems. We first give an overview on the existing LDA regularization techniques. Then, a unified framework for LDA and a combined LDA algorithm for SSS problem are described. Finally, we provide the experimental results and some conclusions.

To solve the Small Sample Size (SSS) problem, the recent linear discriminant analysis using the 2D matrix-based data representation model has demonstrated its superiority over that using the conventional vector-based data representation model in face recognition [7]. But the explicit reason why the matrix-based model is better than vectorized model has not been given until now. In this paper, a framework of Generalized 2D Fisher Discriminant Analysis (G2DFDA) is proposed. Three contributions are included in this framework: 1) the essence of these ’2D’ methods is analyzed and their relationships with conventional ’1D’ methods are given, 2) a Bilateral and 3) a Kernel-based 2D Fisher Discriminant Analysis methods are proposed. Extensive experiment results show its excellent performance.

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.

A modification of kernel discriminant analysis for high-dimensional data—with application to face recognition

Complexity-reduced implementations of complete and null-space-based linear discriminant analysis

iLDA: A new dimensional reduction method for non-Gaussian and small sample size datasets

This paper addresses two LDA problems in face recognition. The first one is small sample size (S3) problem while the second is illumination and pose variations. To overcome the S3 problem, this paper proposes a new method in subspace approach in determining the optimal projection for LDA. Also, an in-depth investigation is conducted on the influence of different illuminations and poses variations. Comparisons with existing LDA-based methods are performed using FERET and Yale Group B face databases. The experimental results show that the proposed method gives the best performance comparing with the existing LDA-based methods for both databases. Moreover, the computational cost of the proposed method is near the same as the existing fastest LDA-based method.

Locality-preserving projection (LPP) is a promising manifold-based dimensionality reduction and linear feature extraction method for face recognition. However, there exist two main issues in traditional LPP algorithm. LPP does not utilize the class label information at the training stage and its performance will be affected for classification tasks. In addition, LPP often suffers from small sample size (3S) problem, which occurs when the dimension of input pattern space is greater than the number of training samples. Under this situation, LPP fails to work. To overcome these two limitations, this paper presents a novel supervised regularization LPP (SRLPP) approach based on a supervised graph and a new regularization strategy. It theoretically proves that regularization matrix [Formula: see text] approaches to the original one as the regularized parameter tends to zero. The proposed SRLPP method is subsequently applied to face recognition. The experiments are conducted on two publicly available face databases, namely ORL database and FERET database. Compared with some existing LDA-based and LPP-based linear feature extraction approaches, experimental results show that our SRLPP approach gives superior performance.

The recently proposed Marginal Fisher Analysis (MFA) achieved high performance for face recognition. However, MFA suffers from the small sample size problem and the optimal basis vectors obtained by the MFA are nonorthogonal. In this paper, we present a new method called Direct Orthogonal Marginal Fisher Analysis (DOMFA), which is able to extract all the orthogonal discriminant vectors simultaneously in the high-dimensional feature space without pre-processing using PCA and does not suffer the small sample size problem. Experimental results on ORL database indicate that the proposed DOMFA method achieves better recognition rate than the MFA method and some other orthogonal feature extraction algorithms.