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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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An Approach for the Implementation of Personalization Recommendation of Text Information Retrieval With TextCC

An Approach for the Implementation of Personalization Recomm...

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2005 International Conference on Neural Networks and Brain(ICNN&B’05)

作者： Zhenya Zhang Shuguang Zhang Xufa Wang Shuangping Chen Hongmei Cheng MOE-Microsoft Key Laboratory of Multimedia Computing and Communication University of Science and Technology of China(USTC) Electronical Engineering & Information Science Department of USTC Statistics&Finance Department of USTC Computer Science Department of USTC Mathematics Department of Anhui Normal University

To implement personalization recommendation of text information retrieval(TR) based in user-focus,TextCC,a feed forward neural network for instantly classification is adopted to classify query results according to user-focuses of a user in the *** results show that the implementation of personalization recommendation with TextCC can lighten the user's burden induced by the work of filtering valid information from vast information in some degree while the time requirement of TR is satisfied very well.

关键词： Web An Approach for the Implementation of Personalization Recommendation of Text Information Retrieval With TextCC

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Fisher+Kernel criterion for discriminant analysis

Fisher+Kernel criterion for discriminant analysis

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Shu Yang Shuicheng Yan Dong Xu Xiaoou Tang Chao Zhang National Laboratory on Machine Perception First Hospital Peking University Beijing China 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

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.

关键词： Kernel Laboratories Asia Face recognition Linear discriminant analysis Design optimization Chaotic communication Multimedia computing Batteries Couplings

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Discriminant analysis with tensor representation

Discriminant analysis with tensor representation

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Shuicheng Yan Dong Xu Qiang Yang Lei Zhang Xiaoou Tang 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 Department of Computer Science Hong Kong University of Science and Technology Hong Kong China 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.

关键词： Tensile stress Iterative algorithms Linear discriminant analysis Scattering Asia Image coding Clustering algorithms Algorithm design and analysis Principal component analysis Unsupervised learning

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Lie Point Symmetries of Differential-Difference Equations

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Communications in Theoretical Physics 2004年第5期41卷 645-648页

作者： DING Wei~1 TANG Xiao-Yan~(2,3) 1 Department of Applied Mathematics,Shanghai Jiao Tong University,Shanghai 200030,China2 Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China3 State key laboratory of scientific and engineering computing,Institute of Computational Mathematics and scientific engineering computing,Academy of Mathematics and System Sciences,the Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

In this paper,the classical Lie group approach is extended to find some Lie point symmetries of differential-difference *** reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

关键词： Lie point symmetry differential-difference equation Kac Moody-Virasoro algebra

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Some perspective on the Large Scale scientific Computation Research

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Science China Mathematics 2004年第Z1期47卷 1-3页

作者： DU Qiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080China

　　The "Large Scale scientific Computation (LSSC) Research"project is one of the State Major Basic Research projects funded by the Chinese Ministry of Science and Technology in the field ofinformation scien... 详细信息

关键词： LSSC Some perspective on the Large Scale scientific Computation Research

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Numerical simulation of Richtmyer-Meshkov instability

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Science China Mathematics 2004年第z1期47卷 234-244页

作者： FU Dexun, MA Yanwen, ZHANG Linbo & TIAN BaolinState key laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China State key laboratory of scientific and engineering computing, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China 1. State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences 100080 Beijing China2. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy of Sciences 100080 Beijing China

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

关键词： R-M instability, direct numerical simulation, shock-interface interaction.

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Construction and Analysis of Structured Preconditioners for Block Two-by-Two Matrices

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Journal of Shanghai University(English Edition) 2004年第4期8卷 397-405页

作者：白中治 State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P.R. China

For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.

关键词： block two-by-two matrix preconditioner modified block relaxation iteration eigenvalue distribution positive definiteness.

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Teracluster LSSC-II--Its designing principles and applications in large scale numerical simulations

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中国科学A辑（英文版） 2004年第z1期47卷 53-68页

作者： Zhang Linbo Chen Shiyi LI Xinliang CAO Jianwen ZHANG Wensheng GONG Xingao State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mechanical Engineering The Johns Hopkins University and Center for Computational Science and Engineering Peking University Beijing 100875 China Institute of Mechanics Chinese Academy of SciencesBeijing 100080 China Parallel Computing Laboratory Institute of Software Chinese Academy of Sciences Beijing 100080 China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Surface Physics Laboratory National Key Laboratory Fudan University Shanghai 200433 Institute of Solid State Physics Chinese Academy of Sciences Hefei 230031 China

The teracluster LSSC-II installed at the State key laboratory of scientific and engineering computing, Chinese Academy of Sciences is one of the most powerful PC clusters in China. It has a peek performance of 2Tflops. With a Linpack performance of 1.04Tflops, it is ranked at the 43rd place in the 20th TOP500 List (November 2002), 51st place in the 21st TOP500 List (June 2003), and the 82nd place in the 22nd TOP500 List (November 2003) with a new Linpack performance of 1.3Tflops. In this paper, we present some design principles of this cluster, as well as its applications in some large-scale numerical simulations.

关键词： high performance computing PC cluster large scale numerical simulations

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A class of globally convergent conjugate gradient methods

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Science China Mathematics 2003年第2期46卷 251-261页

作者：戴彧虹袁亚湘 State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences

Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can beregarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed byDai et al. To analyze this class of methods, we introduce some unified tools that concern a general methodwith the scalarβk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods canuniformly be analyzed.

关键词： unconstrained optimization, conjugate gradient, line search, global convergence.

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