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2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2006

作者： Xu, Dong Lin, Stephen Yan, Shuicheng Tang, Xiaoou MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Microsoft Research Asia Beijing China Department of Information Engineering Chinese University of Hong Kong Hong Kong Hong Kong Department of Electrical Engineering Columbia University United States Beckman Institute University of Illinois Urbana-Champaign United States

ISBN: (纸本)0769525970

In supervised dimensionality reduction, tensor representations of images have recently been employed to enhance classification of high-dimensional data with small training sets. To handle tensor data, this approach has been formulated with tight restrictions on projection directions that, along with convergence issues and the assumption of Gaussian distributed class data, limits its face recognition performance. To overcome these problems, we propose a method of rank-one projections with adaptive margins (RPAM) that gives a provably convergent solution for tensor data over a more general class of projections, while accounting for margins between samples of different classes. In contrast to previous margin based works which determine margin sample pairs within the original high dimensional space, RPAM instead aims to maximize the margins defined in the expected lower dimensional feature subspace by progressive margin refinement after each rank-one projection. In addition to handling tensor data, vector-based variants of RPAM are presented for linear mappings and for nonlinear mappings using kernel tricks. Comprehensive experimental results demonstrate that RPAM brings significant improvement in face recognition over previous subspace learning techniques. © 2006 IEEE.

关键词： Adaptive algorithms

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Rank-one Projections with Adaptive Margins for Face Recognition

Rank-one Projections with Adaptive Margins for Face Recognit...

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Dong Xu S. Lin Shuicheng Yan Xiaoou Tang Department of Electrical Engineering Columbia University USA MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Microsoft Research Asia Beijing China Department of Information Engineering Chinese University of Hong Kong Hong Kong China Beckman Institute University of Illinois Urbana-Champaign Champaign USA

关键词： Face recognition Tensile stress Linear discriminant analysis Asia Computer vision Pattern recognition Scattering Laboratories Multimedia computing Data engineering

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Concurrent subspaces analysis

Concurrent subspaces analysis

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Xu, Dong Yan, Shuicheng Zhang, Lei Zhang, Hong-Jiang Liu, Zhengkai Shum, Heung-Yeung MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

A representative subspace is significant for image analysis, while the corresponding techniques often suffer from the curse of dimensionality dilemma. In this paper, we propose a new algorithm, called Concurrent Subspaces Analysis (CSA), to derive representative subspaces by encoding image objects as 2 nd or even higher order tensors. In CSA, an original higher dimensional tensor is transformed into a lower dimensional one using multiple concurrent subspaces that characterize the most representative information of different dimensions, respectively. Moreover, an efficient procedure is provided to learn these subspaces in an iterative manner. As analyzed in this paper, each sub-step of CSA takes the column vectors of the matrices, which are acquired from the k-mode unfolding of the tensors, as the new objects to be analyzed, thus the curse of dimensionality dilemma can be effectively avoided. The extensive experiments on the 3rd order tensor data, simulated video sequences and Gabor filtered digital number image database show that CSA outper-forms Principal Component Analysis in terms of both reconstruction and classification capability. © 2005 IEEE.

关键词： Image analysis

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Graph embedding: A general framework for dimensionality reduction

Graph embedding: A general framework for dimensionality redu...

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yan, Shuicheng Xu, Dong Zhang, Benyu Zhang, Hong-Jiang Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)769523722

In the last decades, a large family of algorithms - supervised or unsupervised;stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA. © 2005 IEEE.

关键词： Embedded systems

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Fisher+Kernel Criterion for discriminant analysis

Fisher+Kernel Criterion for discriminant analysis

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yang, Shu Yan, Shuicheng Xu, Dong Tang, Xiaoou Zhang, Chao National Laboratory on Machine Perception Peking University Beijing China Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)769523722

We simultaneously approach two tasks of nonlinear discriminant analysis and kernel selection problem by proposing a unified criterion, Fisher+Kernel Criterion. In addition, an efficient procedure is derived to optimize this new criterion in an iterative manner. More specifically, original input vector is first transformed into a higher dimensional feature matrix through a battery of nonlinear mappings involved in different kernels. Then, based on the feature matrices, FKC is presented within two coupled projection spaces: one projection space is used to search for the optimal combinations of kernels; while the other encodes the optimal nonlinear discriminating projection directions. Our proposed method is a unified framework for both kernel selection and nonlinear discriminant analysis. Besides, the algorithm potentially alleviates overfitting problem existing in traditional KDA and has no singularity problems in most cases. The effectiveness of our proposed algorithm is validated by extensive face recognition experiments on several datasets. © 2005 IEEE.

关键词： Pattern recognition

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Implicit curves and surfaces based on BP neural network

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Journal of Information and Computational Science 2005年第2期2卷 259-271页

作者： Li, Daolun Lu, Detang Kong, Xiangyang Wu, Gang Laboratory of Software in Computing and Communication of Anhui Province University of Science and Technology of China Hefei 230026 China Institute of Engineering and Science Software University of Science and Technology of China Hefei 230026 China Nanjing University of Finance and Economics Nanjing 210012 China

Neural networks, combined with implicit polynomials, can be employed to represent 2D curves as well as 3D surfaces. The zero-set of a neural network can be used to describe data points constituting a 2D curve or 3D surface. The neural network fitting algorithms developed in this paper aim to reduce the learning time of neural network by selecting the exterior and interior constraint points simultaneously and improve the fitting performance by using the linear transfer function at the output layers. The neural network adopted so far is a multilayer feed-forward type. Simulation results show that the proposed algorithms provide a significant reduction in learning time, and good fitting results. This paper lays the bases of the neural network modeling approach.

关键词： Computer graphics

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Discriminant analysis with tensor representation

Discriminant analysis with tensor representation

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yan, Shuicheng Xu, Dong Yang, Qiang Zhang, Lei Tang, Xiaoou Zhang, Hong-Jiang Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Department of Computer Science Hong Kong University of Science and Technology Hong Kong Hong Kong Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a Discriminant Tensor Criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode Cluster-based Discriminant Analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm Discriminant Analysis with Tensor Representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes;2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem;and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases. © 2005 IEEE.

关键词： Problem solving

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Graph embedding: a general framework for dimensionality reduction

Graph embedding: a general framework for dimensionality redu...

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Shuicheng Yan Dong Xu Benyu Zhang Hong-Jiang Zhang Department of Information Engineering Chinese University of Hong Kong Sha Tin Hong Kong China MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

In the last decades, a large family of algorithms - supervised or unsupervised; stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA.

关键词： Linear discriminant analysis Statistics Geometry Kernel Algorithm design and analysis Principal component analysis Laplace equations Asia Vectors Laboratories

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Concurrent subspaces analysis

Concurrent subspaces analysis

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Dong Xu Shuicheng Yan Lei Zhang Hong-Jiang Zhang Zhengkai Liu Heung-Yeung Shum MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Department of Information Engineering Chinese University of Hong Kong Sha Tin Hong Kong China Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

A representative subspace is significant for image analysis, while the corresponding techniques often suffer from the curse of dimensionality dilemma. In this paper, we propose a new algorithm, called concurrent subspaces analysis (CSA), to derive representative subspaces by encoding image objects as 2/sup nd/ or even higher order tensors. In CSA, an original higher dimensional tensor is transformed into a lower dimensional one using multiple concurrent subspaces that characterize the most representative information of different dimensions, respectively. Moreover, an efficient procedure is provided to learn these subspaces in an iterative manner. As analyzed in this paper, each sub-step of CSA takes the column vectors of the matrices, which are acquired from the k-mode unfolding of the tensors, as the new objects to be analyzed, thus the curse of dimensionality dilemma can be effectively avoided. The extensive experiments on the 3/sup rd/ order tensor data, simulated video sequences and Gabor filtered digital number image database show that CSA outperforms principal component analysis in terms of both reconstruction and classification capability.

关键词： Tensile stress Image sequence analysis Image analysis Algorithm design and analysis Image coding Analytical models Video sequences Digital filters Gabor filters Image databases

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Coupled kernel-based subspace learning

Coupled kernel-based subspace learning

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Shuicheng Yan Dong Xu Lei Zhang Benyu Zhang HongJiang Zhang Department of Information Engineering Chinese University of Hong Kong Sha Tin Hong Kong China MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

It was prescriptive that an image matrix was transformed into a vector before the kernel-based subspace learning. In this paper, we take the kernel discriminant analysis (KDA) algorithm as an example to perform kernel analysis on 2D image matrices directly. First, each image matrix is decomposed as the product of two orthogonal matrices and a diagonal one by using singular value decomposition; then an image matrix is expanded to be of higher or even infinite dimensions by applying the kernel trick on the column vectors of the two orthogonal matrices; finally, two coupled discriminative kernel subspaces are iteratively learned for dimensionality reduction by optimizing the Fisher criterion measured by Frobenius norm. The derived algorithm, called coupled kernel discriminant analysis (CKDA), effectively utilizes the underlying spatial structure of objects and the discriminating information is encoded in two coupled kernel subspaces respectively. The experiments on real face databases compared with KDA and Fisherface validate the effectiveness of CKDA.

关键词： Kernel Matrix decomposition Algorithm design and analysis Principal component analysis Feature extraction Linear discriminant analysis Image analysis Performance analysis Asia Singular value decomposition

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