Radar Target Recognition Using A Modified Kernel Direct Discriminant Analysis Algorithm

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.

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

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

Classical Linear Discriminant Analysis (LDA) is usually suffers from the small sample size (SSS) problem when dealing with the high dimensional face data. Many methods have been proposed for solving this problem such as Fisherface and Null Space LDA (N-LDA), but these methods are overfitted to the training set and inevitably lose some useful discriminative information in many cases. To effectively utilize nearly all useful discriminative information, a not completely random sampling framework for the integration of multiple features is developed. However, this method has the following main disadvantage: By directly employing feature extraction, the newly constructed variables may contain lots of information originated from those redundant features in the original space. So, in this paper, we introduce a new random sampling LDA by incorporating feature selection for face recognition, that is, some redundant features are removed using the given feature selection methods at first, and then PCA is employed, finally we use random sampling to generate multiple feature subsets. Along this, corresponding weak LDA classifiers are naturally generated and an integrated classifier is developed using a fusion rule. Experiments on 4 face datasets (AR, ORL, Yale, YaleB) show the effectiveness of our algorithm.

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.

This paper presents a novel and effective method for facial expression recognition including happiness, disgust, fear, anger, sadness, surprise, and neutral state. The proposed method utilizes a regularized discriminant analysis-based boosting algorithm (RDAB) with effective Gabor features to recognize the facial expressions. Entropy criterion is applied to select the effective Gabor feature which is a subset of informative and nonredundant Gabor features. The proposed RDAB algorithm uses RDA as a learner in the boosting algorithm. The RDA combines strengths of linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). It solves the small sample size and ill-posed problems suffered from QDA and LDA through a regularization technique. Additionally, this study uses the particle swarm optimization (PSO) algorithm to estimate optimal parameters in RDA. Experiment results demonstrate that our approach can accurately and robustly recognize facial expressions.

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.

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

The time-varying Received Signal Strength (RSS) drastically reduces the correlation between signals and location information, which leads to degrade the indoor positioning accuracy in WiFi. And the kernel selection of Support Vector Regression (SVR) is limited by the Mercer theorem, it has a negative influence on the regressive result. In this paper, a new positioning algorithm based on Kernel Direct Discriminant Analysis (KDDA) and Relevance Vector Regression (RVR) is proposed to resolve these problems. The proposed algorithm employs KDDA to reconstruct the localization information contained in the RSS readings. The most discriminative localization features are then extracted while the redundant localization features and noise are discarded by KDDA. The extracted localization features are taken as inputs to RVR learning machine and the mapping between localization features and physical locations is established. The experimental results show that the proposed algorithm obtains more significant accuracy improvement than existing WKNN methods and KDDA-SVR algorithm.

In this paper, a novel approach, namely kernel projection vector space (KPVS), is proposed for radar target recognition using high-resolution range profile (HRRP). First, the HRRP samples are mapped into a high-dimensional feature space using nonlinear mapping. Second, the kernel projection vectors, are obtained by kernel discriminant analysis. Then, for each class, the kernel projection vector space is formed using all the training kernel projection vectors of class. Finally, the minimum hyper plane distance classifier (MHDC) is used for classification. The aim of KPVS method is to represent the feature area of target using kernel projection vector space, and effectively measure the distance between the test HRRP and feature area via minimum hyper plane distance (MHD) metric. The experimental results of measured data show that the proposed method has better performance of recognition than KPCA and KFDA.

High resolution range profile (HRRP) has the advantages of low complexity in imaging and processing. These features make HRRP widely adopted in radar automatic target recognition technology. Template matching is a representative technique for radar target recognition using HRRP. To overcome the attitude sensitivity problem of HRRP data, it is necessary to subdivide the training database according to attitude domain, and construct corresponding templates for matching. However, templates from traditional methods usually cause the loss of details due to the smoothing process, with limited classification performance. This paper is motivated by proposing a template generation approach based on maximum information profile, which retains the detailed information in templates for accuracy optimization. The proposed method is verified by the recognition experiments of three types of aircraft targets. The experimental results indicate that the maximum information profile outperform the mean range profile contributed by the angle domain template.

To reduce the memory and timing complexity of the Side-Channel Attacks (SCA), dimensionality reduction techniques are usually applied to the measurements. They aim to detect the so-called Points of Interest (PoIs), which are time samples which (jointly) depend on some sensitive information (e.g. secret key sub-parts), and exploit them to extract information. The extraction is done through the use of functions which combine the measurement time samples. Examples of combining functions are the linear combinations provided by the Principal Component Analysis or the Linear Discriminant Analysis. When a masking countermeasure is properly implemented to thwart SCAs, the selection of PoIs is known to be a hard task: almost all existing methods have a combinatorial complexity explosion, since they require an exhaustive search among all possible d-tuples of points. In this paper we propose an efficient method for informative feature extraction in presence of masking countermeasure. This method, called Kernel Discriminant Analysis, consists in completing the Linear Discriminant Analysis with a so-called kernel trick, in order to efficiently perform it over the set of all possible d-tuples of points without growing in complexity with d. We identify and analyse the issues related to the application of such a method. Afterwards, its performances are compared to those of the Projection Pursuit (PP) tool for PoI selection up to a 4th-order context. Experiments show that the Kernel Discriminant Analysis remains effective and efficient for high-order attacks, leading to a valuable alternative to the PP in constrained contexts where the increase of the order d does not imply a growth of the profiling datasets.