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Marginal Fisher Analysis and Its Variants for Human Gait Recognition and Content Based Image Retrieval
"... Abstract—Dimensionality reduction algorithms, which aim to select a small set of efficient and discriminant features, have attracted great attention for human gait recognition and contentbased image retrieval (CBIR). In this paper, we present extensions of our recently proposed marginal Fisher anal ..."
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Cited by 35 (5 self)
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Abstract—Dimensionality reduction algorithms, which aim to select a small set of efficient and discriminant features, have attracted great attention for human gait recognition and contentbased image retrieval (CBIR). In this paper, we present extensions of our recently proposed marginal Fisher analysis (MFA) to address these problems. For human gait recognition, we first present a direct application of MFA, then inspired by recent advances in matrix and tensorbased dimensionality reduction algorithms, we present matrixbased MFA for directly handling 2D input in the form of graylevel averaged images. For CBIR, we deal with the relevance feedback problem by extending MFA to marginal biased analysis, in which withinclass compactness is characterized only by the distances between each positive sample and its neighboring positive samples. In addition, we present a new technique to acquire a direct optimal solution for MFA without resorting to objective function modification as done in many previous algorithms. We conduct comprehensive experiments on the USF HumanID gait database and the Corel image retrieval database. Experimental results demonstrate that MFA and its extensions outperform related algorithms in both applications. Index Terms—Contentbased image retrieval (CBIR), dimensionality reduction, gait recognition, marginal Fisher analysis (MFA), relevance feedback. I.
multimedia retrieval framework based on semisupervised ranking and relevance feedback
 IEEE Trans. Pattern Anal. Mach. Intell
, 2012
"... Abstract—We present a new framework for multimedia content analysis and retrieval which consists of two independent algorithms. First, we propose a new semisupervised algorithm called ranking with Local Regression and Global Alignment (LRGA) to learn a robust Laplacian matrix for data ranking. In L ..."
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Cited by 30 (9 self)
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Abstract—We present a new framework for multimedia content analysis and retrieval which consists of two independent algorithms. First, we propose a new semisupervised algorithm called ranking with Local Regression and Global Alignment (LRGA) to learn a robust Laplacian matrix for data ranking. In LRGA, for each data point, a local linear regression model is used to predict the ranking scores of its neighboring points. A unified objective function is then proposed to globally align the local models from all the data points so that an optimal ranking score can be assigned to each data point. Second, we propose a semisupervised longterm Relevance Feedback (RF) algorithm to refine the multimedia data representation. The proposed longterm RF algorithm utilizes both the multimedia data distribution in multimedia feature space and the history RF information provided by users. A trace ratio optimization problem is then formulated and solved by an efficient algorithm. The algorithms have been applied to several contentbased multimedia retrieval applications, including crossmedia retrieval, image retrieval, and 3D motion/pose data retrieval. Comprehensive experiments on four data sets have demonstrated its advantages in precision, robustness, scalability, and computational efficiency. Index Terms—Contentbased multimedia retrieval, semisupervised learning, ranking algorithm, relevance feedback, crossmedia retrieval, image retrieval, 3D motion data retrieval. Ç 1
Trace ratio criterion for feature selection
 In AAAI
, 2008
"... Fisher score and Laplacian score are two popular feature selection algorithms, both of which belong to the general graphbased feature selection framework. In this framework, a feature subset is selected based on the corresponding score (subsetlevel score), which is calculated in a trace ratio for ..."
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Cited by 24 (3 self)
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Fisher score and Laplacian score are two popular feature selection algorithms, both of which belong to the general graphbased feature selection framework. In this framework, a feature subset is selected based on the corresponding score (subsetlevel score), which is calculated in a trace ratio form. Since the number of all possible feature subsets is very huge, it is often prohibitively expensive in computational cost to search in a brute force manner for the feature subset with the maximum subsetlevel score. Instead of calculating the scores of all the feature subsets, traditional methods calculate the score for each feature, and then select the leading features based on the rank of these featurelevel scores. However, selecting the feature subset based on the featurelevel score cannot guarantee the optimum of the subsetlevel score. In this paper, we directly optimize the subsetlevel score, and propose a novel algorithm to efficiently find the global optimal feature subset such that the subsetlevel score is maximized. Extensive experiments demonstrate the effectiveness of our proposed algorithm in comparison with the traditional methods for feature selection.
TRACE OPTIMIZATION AND EIGENPROBLEMS IN DIMENSION REDUCTION METHODS
"... Abstract. This paper gives an overview of the eigenvalue problems encountered in areas of data mining that are related to dimension reduction. Given some input highdimensional data, the goal of dimension reduction is to map them to a lowdimensional space such that certain properties of the initial ..."
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Cited by 20 (1 self)
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Abstract. This paper gives an overview of the eigenvalue problems encountered in areas of data mining that are related to dimension reduction. Given some input highdimensional data, the goal of dimension reduction is to map them to a lowdimensional space such that certain properties of the initial data are preserved. Optimizing the above properties among the reduced data can be typically posed as a trace optimization problem that leads to an eigenvalue problem. There is a rich variety of such problems and the goal of this paper is to unravel relations between them as well as to discuss effective solution techniques. First, we make a distinction between projective methods that determine an explicit linear projection from the highdimensional space to the lowdimensional space, and nonlinear methods where the mapping between the two is nonlinear and implicit. Then, we show that all of the eigenvalue problems solved in the context of explicit projections can be viewed as the projected analogues of the socalled nonlinear or implicit projections. We also discuss kernels as a means of unifying both types of methods and revisit some of the equivalences between methods established in this way. Finally, we provide some illustrative examples to showcase the behavior and the particular characteristics of the various dimension reduction methods on real world data sets.
Parzen Discriminant Analysis
"... In this paper, we propose a nonparametric Discriminant Analysis method (no assumption on the distributions of classes), called Parzen Discriminant Analysis (PDA). Through a deep investigation on the nonparametric density estimation, we find that minimizing/maximizing the distances between each dat ..."
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Cited by 18 (2 self)
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In this paper, we propose a nonparametric Discriminant Analysis method (no assumption on the distributions of classes), called Parzen Discriminant Analysis (PDA). Through a deep investigation on the nonparametric density estimation, we find that minimizing/maximizing the distances between each data sample and its nearby similar/dissimilar samples is equivalent to minimizing an upper bound of the Bayesian error rate. Based on this theoretical analysis, we define our criterion as maximizing the average local dissimilarity scatter with respect to a fixed average local similarity scatter. All local scatters are calculated in fixed size local regions, resembling the idea of Parzen estimation. Experiments in UCI machine learning database show that our method impressively outperforms other related neighbor based nonparametric methods. 1.
NonNegative Graph Embedding
"... We introduce a general formulation, called nonnegative graph embedding, for nonnegative data decomposition by integrating the characteristics of both intrinsic and penalty graphs [17]. In the past, such a decomposition was obtained mostly in an unsupervised manner, such as Nonnegative Matrix Facto ..."
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Cited by 9 (2 self)
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We introduce a general formulation, called nonnegative graph embedding, for nonnegative data decomposition by integrating the characteristics of both intrinsic and penalty graphs [17]. In the past, such a decomposition was obtained mostly in an unsupervised manner, such as Nonnegative Matrix Factorization (NMF) and its variants, and hence unnecessary to be powerful at classification. In this work, the nonnegative data decomposition is studied in a unified way applicable for both unsupervised and supervised/semisupervised configurations. The ultimate data decomposition is separated into two parts, which separatively preserve the similarities measured by the intrinsic and penalty graphs, and together minimize the data reconstruction error. An iterative procedure is derived for such a purpose, and the algorithmic nonnegativity is guaranteed by the nonnegative property of the inverse of any Mmatrix. Extensive experiments compared with NMF and conventional solutions for graph embedding demonstrate the algorithmic properties in sparsity, classification power, and robustness to image occlusions. 1.
SideInformation based Linear Discriminant Analysis for Face Recognition
"... In recent years, face recognition in the unconstrained environment has attracted increasing attentions, and a few methods have been evaluated on the Labeled Faces in the Wild (LFW) database. In the unconstrained conditions, sometimes we cannot obtain the full class label information of all the subje ..."
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Cited by 9 (3 self)
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In recent years, face recognition in the unconstrained environment has attracted increasing attentions, and a few methods have been evaluated on the Labeled Faces in the Wild (LFW) database. In the unconstrained conditions, sometimes we cannot obtain the full class label information of all the subjects. Instead we can only get the weak label information, such as the sideinformation, i.e., the image pairs from the same or different subjects. In this scenario, many multiclass methods (e.g., the wellknown Fisher Linear Discriminant Analysis (FLDA)), fail to work due to the lack of full class label information. To effectively utilize the sideinformation in such case, we propose SideInformation based Linear Discriminant Analysis (SILD), in which the withinclass and betweenclass scatter matrices are directly calculated by using the sideinformation. Moreover, we theoretically prove that our SILD method is equivalent to FLDA when the full class label information is available. Experiments on LFW and FRGC databases support our theoretical analysis, and SILD using multiple features also achieve promising performance when compared with the stateoftheart methods. 1
Learning a 3D Human Pose Distance Metric from Geometric Pose Descriptor
"... of joint orientations or coordinates, which does not sufficiently reflect the pose similarity of human perception. In this paper we present a new pose distance metric. First, we propose a new rich pose feature set called Geometric Pose Descriptor (GPD). GPD is more effective in encoding pose similar ..."
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Cited by 7 (3 self)
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of joint orientations or coordinates, which does not sufficiently reflect the pose similarity of human perception. In this paper we present a new pose distance metric. First, we propose a new rich pose feature set called Geometric Pose Descriptor (GPD). GPD is more effective in encoding pose similarity by utilizing features on geometric relations among body parts, as well as temporal information such as velocities and accelerations. Based on GPD, we propose a semisupervised distance metric learning algorithm called Regularized Distance Metric Learning with Sparse Representation (RDSR), which integrates information from both unsupervised data relationship and labels. We apply the proposed pose distance metric to applications of motion transition decision and content based pose retrieval. Quantitative evaluations demonstrate that our method achieves better results with only a small amount of human labels, showing that the proposed pose distance metric is a promising building block for various 3D motion related applications. Index Terms—human motion, character animation, pose features, distance metric, semisupervised learning. 1
Classification via semiRiemannian spaces
 in Proc. IEEE Conf. on Computer Vision and Pattern Recognition
, 2008
"... In this paper, we develop a geometric framework for linear or nonlinear discriminant subspace learning and classification. In our framework, the structures of classes are conceptualized as a semiRiemannian manifold which is considered as a submanifold embedded in an ambient semiRiemannian space. T ..."
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Cited by 6 (4 self)
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In this paper, we develop a geometric framework for linear or nonlinear discriminant subspace learning and classification. In our framework, the structures of classes are conceptualized as a semiRiemannian manifold which is considered as a submanifold embedded in an ambient semiRiemannian space. The class structures of original samples can be characterized and deformed by local metrics of the semiRiemannian space. SemiRiemannian metrics are uniquely determined by the smoothing of discrete functions and the nullity of the semiRiemannian space. Based on the geometrization of class structures, optimizing class structures in the feature space is equivalent to maximizing the quadratic quantities of metric tensors in the semiRiemannian space. Thus supervised discriminant subspace learning reduces to unsupervised semiRiemannian manifold learning. Based on the proposed framework, a novel algorithm, dubbed as SemiRiemannian Discriminant Analysis (SRDA), is presented for subspacebased classification. The performance of SRDA is tested on face recognition (singular case) and handwritten capital letter classification (nonsingular case) against existing algorithms. The experimental results show that SRDA works well on recognition and classification, implying that semiRiemannian geometry is a promising new tool for pattern recognition and machine learning. 1.
WorstCase Linear Discriminant Analysis
"... Dimensionality reduction is often needed in many applications due to the high dimensionality of the data involved. In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis (LDA) model and note that the formulation is based on the averagecase view. B ..."
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Cited by 5 (0 self)
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Dimensionality reduction is often needed in many applications due to the high dimensionality of the data involved. In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis (LDA) model and note that the formulation is based on the averagecase view. Based on this analysis, we then propose a new dimensionality reduction method called worstcase linear discriminant analysis (WLDA) by defining new betweenclass and withinclass scatter measures. This new model adopts the worstcase view which arguably is more suitable for applications such as classification. When the number of training data points or the number of features is not very large, we relax the optimization problem involved and formulate it as a metric learning problem. Otherwise, we take a greedy approach by finding one direction of the transformation at a time. Moreover, we also analyze a special case of WLDA to show its relationship with conventional LDA. Experiments conducted on several benchmark datasets demonstrate the effectiveness of WLDA when compared with some related dimensionality reduction methods. 1