Fuzzy 2DLDA for Face Recognition

Feature extraction based on fuzzy 2DLDA

This paper presents a new method for image feature extraction, namely, the fuzzy 2D discriminant locality preserving projections (F2DDLPP) based on the 2D discriminant locality preserving projections (2DDLPP) and fuzzy set theory. Firstly, we calculate the membership degree matrix by fuzzy k-nearest neighbor (FKNN), then we incorporate the membership degree matrix into the definition of the intra-class scatter matrix and inter-class scatter matrix, respectively. Secondly, we can get the fuzzy intra-class scatter matrix and fuzzy inter-class scatter matrix, respectively. The FKNN is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices. So, F2DDLPP can extract discriminative features from overlapping (outlier) samples which is different to the conventional 2DDLPP. Finally, Experiments on the Yale, ORL face databases, USPS database and PolyU palmprint database are demonstrated to verify the effectiveness of the proposed algorithm.

Fuzzy MSD based feature extraction method for face recognition

In fuzzy clustering, we always use fuzzy equivalence matrix to find the clustering results. Although fuzzy equivalence matrix is one of the most important tools in fuzzy clustering, it’s hard to judge whether a fuzzy matrix is a fuzzy equivalence matrix directly. In this paper, some simple and useful properties of the fuzzy equivalence matrices have been proposed based on the basic properties proposed in the classi cal articles. Using these properties, the judgment whether a fuzzy matrix is a fuzzy equivalence matrix may become an easy work. Keywords: Fuzzy clustering, fuzzy equivalence matrix 1. INTRODUCTION Given a finite set of objects X, and a measure of similarity for an arbitrary pair of objects, the problem of clustering is to find a partition of X such that the degree of similarity is high for objects within each block (cluster) and low for objects in different blocks. The purpose of clustering is to find a natural classification of given objects on the basis of a conceived concept of similarity. The classification may help to uncover a structure in given data, improve our understanding of a complex system, or suggest a meaningful simplification of a given system [1]. The requirement that given objects be classified into pairwise disjoint subsets (crisp clusters) is overly strong in many practical applications. Fuzzy set theory allows us to weaken it and, hence, make clustering more realistic. So, fuzzy clustering becomes one of the hottest research branches of data mining. One of the approaches to fuzzy clustering is based on fuzzy equivalence relations defined on X. Every fuzzy equivalence relation induces a crisp partition in each of its .-cuts. Using this approach, the fuzzy clustering problem becomes the problem of identifying a fuzzy equivalence relation on X in terms of a conceived concept of similarity. Although this may not be possible to do directly, it is usually easy to determine a fuzzy compatibility relation in terms of an appropriate distance function defined on X. A distance function is always reflexive and symmetric, but it is not transitive. However, once we have a compatibility relation, we can readily obtain a meaningful fuzzy equivalence relation by calculating its transitive closure. The resulting fuzzy equivalence relation offers the user a sequence of crisp partitions on X, which are linearly ordered by refinement ordering and graded by values of . [0, 1]. The user is given a flexibility to choose one of these partitions on the basis of additional criteria [2-4]. But, to calculate the transitive closure of a N×N fuzzy matrix , we need to calculate the 2kth power of the matrix, where k = 1, 2, , N. In the processing, after we calculate the 2k+1th power of the matrix and find that the 2k+1th power of the matrix is equal to the 2kth power of the matrix, the 2kth power of the matrix is the transitive closure of the matrix. In fact, if we can find the 2kth power of the matrix is a fuzzy equivalence matrix directly, we do not need to calculate the 2k+1th power of the matrix. If we can judge a fuzzy matrix is a fuzzy equivalence matrix by means of some simple properties of the equivalence matrix, it may be helpful. In this paper, some properties of the fuzzy equivalence matrix have been proposed and the judgment whether a fuzzy *white70121@163.com

In this paper, we propose an extended multiple discriminant analysis (EMDA) method to solve the feature extraction problem in high dimensional pattern space for multiple classes discrimination. The proposed method can be seen as an extension of the traditional multiple discriminant analysis (MDA) method. which requires that the within-class scatter matrix is nonsingular. However, we may face many discriminant problems that do not satisfy this condition, such as the face recognition where the within-class matrix is often singular. To solve this problem, we extend the traditional MDA method and propose the EMDA method. The feature extraction strategy of the EMDA method is to maximize the trace of the between-class scatter matrix while constrains the trace of the within-class scatter matrix to be zero. However, to find the solution of the EMDA turns out to be a difficult task. In this paper, we find a way to overcome this problem. With the ORL face database, experiments show that the EMDA method reaches the lowest average class error rate compared to the eigenface method and the Fisherface method, which is only 49.9% of that the traditional eigenface and 79.4% of that the Fisherface method.

Fault detection based on robust characteristic dimensionality reduction

Linear Discriminant Analysis (LDA) [1] is a well-known method for face recognition in feature extraction and dimension reduction. To solve the “small sample” effect of LDA, Two-Dimensional Linear Discriminant Analysis (2DLDA) [2] has been used for face recognition recently，but its could hardly take use of the relationship between the adjacent scatter matrix. In this paper, I improved the between-class scatter matrix, proposed paired-class scatter matrix for face representation and recognition. In this new method, a paired between-class scatter matrix distance metric is used to measure the distance between random paired between-class scatter matrix. To test this new method, ORL face database is used and the results show that the paired between-class scatter matrix based 2DLDA method （N2DLDA） outperforms the 2DLDA method and achieves higher classification accuracy than the 2DLDA algorithm.

Linear discrimination analysis (LDA) technique is an important and well-developed area of image recognition and to date many linear discrimination methods have been put forward. Despite these efforts, there persist in the traditional LDA some weaknesses. In this paper, we propose a new LDA-based method that can overcome the drawback existed in the traditional LDA method. It redefines the between-class scatter by adding a weight function according to the between-class distance, which helps to separate the classes as much as possible. At the same time, in this method, we firstly remove the null space of total scatter matrix which has been proved to be the common null space of both between-class and within-class scatter matrix, and useless for discrimination. Then in the lower-dimensional projected space, the null space of the resulting within-class scatter matrix is calculated. This lower-dimensional null space, combined with the previous projection, represents a subspace of the whole null space of within-class scatter matrix, and is really useful for discrimination. The optimal discriminant vectors of LDA are derived from it. Experiment results show our method achieves better performance in comparison with the traditional LDA methods.

Fuzzy concepts are represented by fuzzy sets, so a fuzzy knowledge is defined to be a collection of fuzzy sets (concepts) which includes two constants, 1 (true) and 0 (false). Abstractly, a logical derivation is a finite series of logical operations acting on a given knowledge. In fuzzy world, logical operations are defined by mathematical operations. So fuzzy logical derivations are mathematical derivations, and vice versa In this paper, the closure of fuzzy reasoning is characterized by fuzzy rough sets, and by topologies (neighborhood systems). A new fuzzy concept F N is derivable from the old knowledge K iff the membership function of F N is continuous in K-topology, or equivalently, iff F N is a rough fuzzy set (concept) of I N D(K),or plainly, iff the membership function of F N is a “step” function in the sense that it takes a constant value in each equivalence class of I N D(K).A fuzzy set L partitions the universe into equivalence classes; each equivalence class consists of those elements which have the same degree of membership. The indiscernibility relation I N D(K)over K is the “intersection” of all the equivalence relations induced by the fuzzy sets in K. The membership function of a fuzzy set is a real valued function, so U can be given the minimal topology such that the membership function of each fuzzy set in K is a continuous function. Such topology is called K-topology.

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic fuzzy sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

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.

In Fisher Linear Discriminant (FLD), the within-class scatter matrix is always singular. To overcome the above problem and preserve discriminatory information, a new method for palm-dorsa vein feature extraction based on Two-Dimensional FLD (2DFLD) is presented in this paper. We applied PCA, PCA+FLD and 2DFLD to extract the palm-dorsa vein feature subspace. The images to be recognized were projected onto the low-dimensional subspace. A classifier to vein matching based on cosine distance was used. Experimental results suggested that the recognition rate of PCA+FLD is about 4.84% higher than that of PCA. Compared with PCA+FLD, 2DFLD is able to yield recognition rate as high as 98.44%, with accuracy enhanced by 7.51%, while the feature extraction time is only 0.4 s. It was demonstrated that the algorithm is effective and quick.

In this paper, a reformative scatter difference discriminant criterion (SDDC) with fuzzy set theory is studied. The scatter difference between between-class and within-class as discriminant criterion is effective to overcome the singularity problem of the within-class scatter matrix due to small sample size problem occurred in classical Fisher discriminant analysis. However, the conventional SDDC assumes the same level of relevance of each sample to the corresponding class. So, a fuzzy maximum scatter difference analysis (FMSDA) algorithm is proposed, in which the fuzzy k-nearest neighbor (FKNN) is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices which are different to the conventional SDDC and effective to extract discriminative features from overlapping (outlier) samples. Experiments conducted on FERET face databases demonstrate the effectiveness of the proposed method.

Hyperspectral image provides abundant spectral information for remote discrimination of subtle differences in ground covers. However, the increasing spectral dimensions, as well as the information redundancy, make the analysis and interpretation of hyperspectral images a challenge. Feature extraction is a very important step for hyperspectral image processing. Feature extraction methods aim at reducing the dimension of data, while preserving as much information as possible. Particularly, nonlinear feature extraction methods (e.g. kernel minimum noise fraction (KMNF) transformation) have been reported to benefit many applications of hyperspectral remote sensing, due to their good preservation of high-order structures of the original data. However, conventional KMNF or its extensions have some limitations on noise fraction estimation during the feature extraction, and this leads to poor performances for post-applications. This paper proposes a novel nonlinear feature extraction method for hyperspectral images. Instead of estimating noise fraction by the nearest neighborhood information (within a sliding window), the proposed method explores the use of image segmentation. The approach benefits both noise fraction estimation and information preservation, and enables a significant improvement for classification. Experimental results on two real hyperspectral images demonstrate the efficiency of the proposed method. Compared to conventional KMNF, the improvements of the method on two hyperspectral image classification are 8 and 11%. This nonlinear feature extraction method can be also applied to other disciplines where high-dimensional data analysis is required.

In order to improve the recognition and detection ability of movie and TV 3D animation images, a method of movie and TV 3D animation image information fusion and feature extraction based on dynamic information fusion and edge contour feature detection is proposed. Establishing a visual information acquisition model of a movie and television three-dimensional animation image, performing corner detection and feature point extraction of the movie and television three-dimensional animation image by adopting a key feature point matching method, extracting dynamic information feature quantity of the edge of the movie and television three-dimensional animation image, combining saliency detection, feature fusion and optimal segmentation of the movie and television three-dimensional animation image, establishing a super-resolution reconstruction feature distribution set of the movie and television three-dimensional animation image. The edge information space region fusion method is used to fuse pixel information and optimize feature reorganization of movie and television three-dimensional animation images. The fuzzy feature distribution set of movie and television three-dimensional animation images is extracted. The information fusion and feature extraction of movie and television three-dimensional animation images are realized by combining wavelet multi-layer decomposition algorithm. The simulation results show that the feature resolution capability of using this method for information fusion and feature extraction of movie and TV 3D animation images is higher, and the output peak signal-to-noise ratio of movie and TV 3D animation image reconstruction is improved.