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Learning linear PCA with convex semi-definite programming

PATTERN RECOGNITION 2007年第10期40卷 2633-2640页

作者： Tao, Qing Wu, Gao-wei Wang, Jue Chinese Acad Sci Inst Automat Lab Complex Syst & Intelligence Sci Beijing 100080 Peoples R China New Star Res Inst Appl Tech Hefei 230031 Peoples R China Chinese Acad Sci Inst Comp Technol Div Intelligent Software Syst Beijing 100080 Peoples R China

The aim of this paper is to learn a linear principal component using the nature of support vector machines (SVMs). To this end, a complete SVM-like framework of linear PCA (SVPCA) for deciding the projection direction is constructed, where new expected risk and margin are introduced. Within this framework, a new semi-definite programming problem for maximizing the margin is formulated and a new definition of support vectors is established. As a weighted case of regular PCA, our SVPCA coincides with the regular PCA if all the samples play the same part in data compression. Theoretical explanation indicates that SVPCA is based on a margin-based generalization bound and thus good prediction ability is ensured. Furthermore, the robust form of SVPCA with a interpretable parameter is achieved using the soft idea in SVMs. The great advantage lies in the fact that SVPCA is a learning algorithm without local minima because of the convexity of the semi-definite optimization problems. To validate the performance of SVPCA, several experiments are conducted and numerical results have demonstrated that their generalization ability is better than that of regular PCA. Finally, some existing problems are also discussed. (c) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： principal component analysis statistical learning theory support vector machines margin maximal margin algorithm semi-definite programming robustness

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A semi-definite programming approach to spatial decorrelation of independently polarized signals

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WIRELESS COMMUNICATIONS & MOBILE COMPUTING 2007年第1期7卷 91-101页

作者： Nordebo, Sven Mohammed, Abbas Vaxjo Univ S-35195 Vaxjo Sweden Blekinge Inst Technol S-37225 Ronneby Sweden

A MIMO channel spatial decorrelation scheme based on semi-definite programming is introduced. As a particular application example, the paper addresses the potential gain of using multiple antennas and MIMO-OFDM techniques in order to increase the bandwidth efficiency in satellite communication systems. In particular, we consider the increase in channel capacity that is possible by exploiting satellite and polarization diversity. A fundamental case is studied with three satellite branches, and where each transmit/receive antenna unit consists of six elemental electric and magnetic dipoles yielding six distinguishable parallel polarization channels per frequency. The numerical examples show that capacity increases linearly on a logarithmic signal-to-noise ratio scale where the constant of proportionality is the number of active parallel channels. In this respect, the simultaneous use of triple electric and triple magnetic dipoles has the potential to triple the capacity of an antenna system based on antenna units of single dipoles. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： semi-definite programming polarization antennas satellite communications MIMO-communications

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Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems

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MATHEMATICAL programming 2007年第2-3期109卷 445-475页

作者： Freund, Robert M. Ordonez, Fernando Toh, Kim-Chuan Univ So Calif Los Angeles CA 90089 USA MIT Alfred P Sloan Sch Management Cambridge MA 02142 USA Natl Univ Singapore Dept Math Singapore 117543 Singapore Singapore MIT Alliance Singapore 117576 Singapore

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the sample correlation (CORR) between these measures and IPM iteration counts (solved using the software SDPT3) when these measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.901), and provides a very good explanation of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.

关键词： behavioral measure condition number degeneracy complementarity interior-point method semi-definite programming

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Set-membership filtering for polytopic uncertain discrete-time systems

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INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 2011年第7期40卷 741-754页

作者： Yang, Fuwen Li, Yongmin E China Univ Sci & Technol Key Lab Adv Control & Optimizat Chem Proc Minist Educ Sch Informat Sci & Engn Shanghai 200237 Peoples R China Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England

In this paper, a set-membership filtering problem is considered for systems with polytopic uncertainty. A recursive algorithm for calculating an ellipsoid which always contains the state is developed. In the prediction step, a predicted state ellipsoid is determined;in the update step, a state estimation ellipsoid is computed by combining the predicted state ellipsoid and the set of states compatible with the measurement equation. A smallest possible estimate set is calculated recursively by solving the semi-definite programming problems. Hence, the proposed set-membership filter relies on a two-step prediction-correction structure, which is similar to the Kalman filter. Simulation results are provided to demonstrate the effectiveness of the proposed method.

关键词： set-membership filtering predicted state ellipsoid state estimation ellipsoid polytopic uncertainty semi-definite programming

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Design of diamond and circular filters by semi-definite programming

Design of diamond and circular filters by semi-definite prog...

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IEEE International Symposium on Circuits and Systems

作者： Hung, T. Q. Tuan, H. D. Nguyen, T. Q. Univ New S Wales Sch Elect Eng & Telecom Sydney NSW 2052 Australia Univ Calif San Diego Dept Elect & Comp Engn San Diego CA 92093 USA

ISBN: (纸本)9781424409204

A new design for linear phase diamond-shaped (DS) and circular-shaped (CS) 2-D filters is developed. First, the frequency masks are efficiently constrained by 2-D second-order trigonometric polynomials. Then semi-definite program ming (SDP) of reasonably low dimension is employed to effectively express the filter specifications. Several numerical examples are provided to demonstrate the superior performance of our design in comparison with all other existing designs.

关键词： polynomials two-dimensional digital filters 2D second-order trigonometric polynomials circular-shaped 2D filters frequency masks linear phase diamond-shaped 2D filters semi-definite programming

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NEW ROBUST UNSUPERVISED SUPPORT VECTOR MACHINES

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Journal of Systems Science & Complexity 2011年第3期24卷 466-476页

作者： Kun ZHAO Mingyu ZHANG ~ Naiyang DENG Logistics School Beijing Wuzi University Beijing 101149 China. School of Economic and Management Beijing Jiaotong University Beijing 100044 China. College of Science China Agricultural University Bcijing 100083 China.

This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite progra... 详细信息

关键词： Robust semi-definite programming support vector machines unsupervised learning

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Pre-Equalization for Pre-Rake DS-UWB Systems with Spectral Mask Constraints

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IEEE TRANSACTIONS ON COMMUNICATIONS 2011年第3期59卷 780-791页

作者： Mohsenian-Rad, Amir-Hamed Mietzner, Jan Schober, Robert Wong, Vincent W. S. Texas Tech Univ Dept Elect & Comp Engn Lubbock TX 79409 USA Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada

In this paper, we propose a novel optimization-based pre-equalization filter (PEF) design framework for direct-sequence ultra-wideband (DS-UWB) systems with pre-Rake combining. The key feature in our design is that we explicitly take into account the spectral mask constraints that are usually imposed in practice by the telecommunications regulation and standardization bodies. This avoids the need for an inefficient power back-off, which is necessary for the existing pre-Rake-based transmitter structures designed solely based on average transmit power constraints. We consider two PEF design structures. In the first structure, the PEF is placed before the up-sampling unit at the transmitter. In the second structure, the PEF is placed after the up-sampling unit. We show that these two structures are significantly different in terms of their capabilities in reducing the residual inter-symbol interference at the receiver and also in following the spectral mask at the transmitter. This introduces a trade-off such that one design structure outperforms the other one, depending on the system parameters. In this regard, we show that if the spreading factor is large enough, the second design structure has a superior performance. Simulation results confirm that both of the proposed PEF structures lead to significant performance gains over PEF designs without explicit spectral mask considerations. In addition, our PEF designs have the capability of adhering to spectral masks with arbitrary shapes.

关键词： Spectral mask constraints pre-equalization pre-Rake combining ultra-wideband communication intersymbol interference optimization semi-definite programming

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Integrating outlier filtering in large margin training

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第5期12卷 362-370页

作者： Xi-chuan ZHOU Hai-bin SHEN Jie-ping YE College of Communication Engineering Chongqing University Chongqing 400044 China School of Electrical Engineering Zhejiang University Hangzhou 310027 China Dcpartment of Computer Science and Engineering Arizona State University Tempe 85281 USA

Large margin classifiers such as support vector machines (SVM) have been applied successfully in various classification ***,their performance may be significantly degraded in the presence of *** this paper,we propose a robust SVM formulation which is shown to be less sensitive to *** key idea is to employ an adaptively weighted hinge loss that explicitly incorporates outlier filtering in the SVM training,thus performing outlier filtering and classification *** resulting robust SVM formulation is *** first relax it into a semi-definite programming which admits a global *** improve the efficiency,an iterative approach is *** have performed experiments using both synthetic and real-world *** show that the performance of the standard SVM degrades rapidly when more outliers are included,while the proposed robust SVM training is more stable in the presence of outliers.

关键词： Support vector machines Outlier filter semi-definite programming Multi-stage relaxation

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Transmit beamforming and interference shaping in cellular cognitive radio networks

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IET COMMUNICATIONS 2011年第14期5卷 2052-2058页

作者： Akhtar, A. M. Nakhai, M. R. Kings Coll London Ctr Telecommun Res Strand WC2R 2LS England

Optimising the quality-of-service for secondary users and minimising interference to the primary users are two important objectives of cognitive radio networks. In this study, the authors address these issues by introducing interference shaping criteria into orthogonal transmit beamforming (OTBF) strategies. Then, the authors formulate this problem using semi-definite programming (SDP) and find the optimal beamforming weight vectors at the secondary base station. The authors also introduce a resource allocation strategy which enables the base station to ensure a weighted fairness among the secondary users, hence, optimising the network for heterogeneous traffic patterns. The authors show that in terms of satisfying the signal-to-interference-plus-noise-ratio (SINR) requirements at the secondary users, their modified maximin SINR and modified minimum transmit power strategies produce fairly close results at the same transmit powers. However, in terms of minimising interference seen by the primary users, the former outperforms the latter. Finally, the authors study the impact of various interference shaping margins (ISMs) on the OTBF strategies. The authors show that the allocated power by the modified minimum transmit power strategy and the SINRs achieved by the modified maximin SINR strategy are inversely and directly proportional with the ISMs, respectively.

关键词： array signal processing Electromagnetic compatibility and interference quality of service cellular radio resource allocation Mobile radio systems signal-to-interference-plus-noise-ratio cognitive radio semi-definite programming orthogonal transmit beamforming cellular cognitive radio networks optimal beamforming weight vectors quality-of-service Signal processing and detection SINR interference (signal) heterogeneous traffic patterns interference shaping margins

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Graph-Theoretic Analysis and Synthesis of Relative Sensing Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第5期56卷 971-982页

作者： Zelazo, Daniel Mesbahi, Mehran Univ Stuttgart Inst Syst Theory & Automat Control D-70550 Stuttgart Germany Univ Washington Dept Aeronaut & Astronaut Seattle WA 98195 USA

This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its H-2 and H-infinity performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H-2 and H-infinity performance are derived. The H-2 performance turns out to be a function of the number of edges in the graph, whereas the H-infinity performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for H-2 performance, and a semi-definite program for the H-infinity performance of uncertain RSNs.

关键词： Combinatorial optimization graph theory H-2 and H-infinity performance relative sensing networks semi-definite programming

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