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A Family of Simple Non-Parametric Kernel Learning Algorithms

JOURNAL OF MACHINE LEARNING RESEARCH 2011年第4期12卷 1313-1347页

作者： Zhuang, Jinfeng Tsang, Ivor W. Hoi, Steven C. H. Nanyang Technol Univ Sch Comp Engn 50 Nanyang Ave Singapore 639798 Singapore

Previous studies of Non-Parametric Kernel Learning (NPKL) usually formulate the learning task as a semi-definite programming (SDP) problem that is often solved by some general purpose SDP solvers. However, for N data examples, the time complexity of NPKL using a standard interior-point SDP solver could be as high as O(N-6.5), which prohibits NPKL methods applicable to real applications, even for data sets of moderate size. In this paper, we present a family of efficient NPKL algorithms, termed "SimpleNPKL", which can learn non-parametric kernels from a large set of pairwise constraints efficiently. In particular, we propose two efficient SimpleNPKL algorithms. One is SimpleNPKL algorithm with linear loss, which enjoys a closed-form solution that can be efficiently computed by the Lanczos sparse eigen decomposition technique. Another one is SimpleNPKL algorithm with other loss functions (including square hinge loss, hinge loss, square loss) that can be re-formulated as a saddle-point optimization problem, which can be further resolved by a fast iterative algorithm. In contrast to the previous NPKL approaches, our empirical results show that the proposed new technique, maintaining the same accuracy, is significantly more efficient and scalable. Finally, we also demonstrate that the proposed new technique is also applicable to speed up many kernel learning tasks, including colored maximum variance unfolding, minimum volume embedding, and structure preserving embedding.

关键词： non-parametric kernel learning semi-definite programming semi-supervised learning side information pairwise constraints

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On Cooperative Relaying Schemes for Wireless Physical Layer Security

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2011年第10期59卷 4985-4997页

作者： Li, Jiangyuan Petropulu, Athina P. Weber, Steven Rutgers State Univ Dept Elect & Comp Engn New Brunswick NJ 08854 USA Drexel Univ Philadelphia PA 19104 USA

We consider a cooperative wireless network in the presence of one or more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme, cooperating nodes retransmit a weighted version of the source signal in a decode-and-forward (DF) fashion. In the second scheme, referred to as cooperative jamming (CJ), while the source is transmitting, cooperating nodes transmit weighted noise to confound the eavesdropper. We investigate two objectives: i) maximization of the achievable secrecy rate subject to a total power constraint and ii) minimization of the total power transmit power under a secrecy rate constraint. For the first design objective, we obtain the exact solution for the DF scheme for the case of a single or multiple eavasdroppers, while for the CJ scheme with a single eavesdropper we reduce the multivariate problem to a problem of one variable. For the second design objective, existing work introduces additional constraints in order to reduce the degree of difficulty, thus resulting in suboptimal solutions. Our work raises those constraints, and obtains either an analytical solution for the DF scheme with a single eavesdropper, or reduces the multivariate problem to a problem of one variable for the CJ scheme with a single eavesdropper. Numerical results are presented to illustrate the proposed results and compare them to existing work.

关键词： Node cooperation physical layer based security secrecy rate semi-definite programming

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Employing multiple-kernel support vector machines for counterfeit banknote recognition

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APPLIED SOFT COMPUTING 2011年第1期11卷 1439-1447页

作者： Yeh, Chi-Yuan Su, Wen-Pin Lee, Shie-Jue Natl Sun Yat Sen Univ Dept Elect Engn Kaohsiung 804 Taiwan

Finding an efficient method to detect counterfeit banknotes is an imperative task in business transactions. In this paper, we propose a system based on multiple-kernel support vector machines for counterfeit banknote recognition. A support vector machine (SVM) to minimize false rates is developed. Each banknote is divided into partitions and the luminance histograms of the partitions are taken as the input of the system. Each partition is associated with its own kernels. Linearly weighted combination is adopted to combine multiple kernels into a combined matrix. Optimal weights with kernel matrices in the combination are obtained through semi-definite programming (SDP) learning. Two strategies are adopted to reduce the amount of time and space required by the SDP method. One strategy assumes the non-negativity of the kernel weights, and the other one is to set the sum of the weights to be unity. Experiments with Taiwanese banknotes show that the proposed approach outperforms single-kernel SVMs, standard SVMs with SDP, and multiple-SVM classifiers. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Banknote recognition Support vector machine Balanced error rate Multiple-kernel learning semi-definite programming

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Maximizing SINR in DL MU-MIMO System on SDP Algorithm

Maximizing SINR in DL MU-MIMO System on SDP Algorithm

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2012 IEEE 14th International Conference on Communication Technology

作者： Yuhua Guo Wenbao Ai School of Science Beijing University of Posts and Tele-communications

ISBN: (纸本)9781467321006

In this paper a semi-definite programming (SDP) algorithm is considered for solving a non-convex quadratic optimization problem with inequality *** algorithm is used for a model of maximizing signal to interference and noise ratio (SINR) with the constraint of each user’s transmitted power in the downlink multiuser multiple-input and multiple-output (DL MU-MIMO) system that can get the optimal value of each user’s *** with the block diagonalization (BD) method and the Generalized Zero-Forcing Channel Inversion (GZI) method,the SDP algorithm shows better performance.

关键词： signal to interference and noise ratio semi-definite programming ratio of quadratic functions optimization model uplink and downlink duality

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DISTRIBUTED NETWORK BEAMFORMING WITH A MULTI-ANTENNA RECEIVER

DISTRIBUTED NETWORK BEAMFORMING WITH A MULTI-ANTENNA RECEIVE...

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12th IEEE International Workshop on Signal Processing Advances in Wireless Communications

作者： Law, Ka L. Gershman, Alex B. Shahbazpanahi, Shahram Tech Univ Darmstadt Commun Syst Grp D-64283 Darmstadt Germany Univ Ontario Inst Technol Fac Engn & Appl Sci Oshawa ON L1H 7K4 Canada

ISBN: (纸本)9781424493326

We consider the problem of distributed beamforming in a relay network, which consists of a single-antenna transmitter, a multi-antenna receiver, and multiple single-antenna relays. Assuming that the channel state information (CSI) is available, our goal is to maximize the destination quality-of-service (QoS) under the total relay transmitted power constraint. Using the semi-definite relaxation (SDR) technique, the problem is turned into a convex semi-definite programming (SDP) problem, which can be solved efficiently using interior point methods. Simulation results show that the proposed relay network beamforming approach offers considerable performance improvements as compared to the single-antenna receiver case.

关键词： Distributed beamforming relay networks semi-definite programming

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Optimum Multi-user Detection by Nonsmooth Optimization

Optimum Multi-user Detection by Nonsmooth Optimization

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Tuan, H. D. Son, T. T. Tuy, H. Nguyen, H. H. Univ New S Wales Sydney NSW 2071 Australia Toyota Technol Inst Nagoya Aichi 468 Japan Inst Matemat Hanoi 10307 Vietnam Univ Saskatchewan Saskatoon SK Canada

ISBN: (纸本)9781457705397

The optimum multiuser detection (OMD) is a discrete (binary) optimization. The previously developed approaches often relax it by a semi-definite program (SDP) and then employ randomization for searching the optimal solution around the solution of this relaxed SDP. In this paper, we show the limited capacity of this SDP program, which at the end cannot give a better solution than the simple linear minimum mean square error detector (LMMSE). Our departure point is to express the problem as quadratic minimization over quadratic equality constraint (QMQE) or concave quadratic minimization over a box of continuous optimization (CQOB). The QMQE allows us to develop a nonsmooth optimization algorithm to locate the global optimal solution of OMD, while CQOB facilities effective confirmation of the solutions found by QMQE. Our intensive simulation clearly shows that the algorithm outperforms all previously developed algorithms while the computational burden is essentially reduced.

关键词： Multiuser detection semi-definite programming concave programming nonsmooth optimization

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Distance metric learning with eigenvalue optimization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2012年第1期13卷

作者： Yiming Ying Peng Li College of Engineering Mathematics and Physical Sciences University of Exeter Exeter UK Department of Engineering Mathematics University of Bristol Bristol UK

The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (Weinberger et al., 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW).

关键词： convex optimization eigenvalue optimization face verification first-order methods matrix factorization metric learning semi-definite programming

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Optimum Multi-user Detection by Nonsmooth Optimization

Optimum Multi-user Detection by Nonsmooth Optimization

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： H.D. Tuan T.T. Son H. Tuy H.H. Nguyen University of New South Wales Sydney NSW 2071 Australia Toyota Technological Institute Nagoya 468-8511 Japan Institute of Mathematics 18 Hoang Quoc Viet 10307 Hanoi Vietnam University of Saskatchewan Saskatoon Canada

ISBN: (纸本)9781457705380

关键词： Multiuser detection semi-definite programming concave programming nonsmooth optimization

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Outlier detection and robust covariance estimation using mathematical programming

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2010年第4期4卷 301-334页

作者： Nguyen, Tri-Dzung Welsch, Roy E. UIUC Newmark Civil Engn Lab 3103 Urbana IL 61801 USA MIT Sloan Sch Management Ctr Computat Res Econ & Management Sci Cambridge MA 02139 USA

The outlier detection problem and the robust covariance estimation problem are often interchangeable. Without outliers, the classical method of maximum likelihood estimation (MLE) can be used to estimate parameters of a known distribution from observational data. When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them. Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions. However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance. An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given smaller weights and can be detected. This method produces a covariance estimator that has the following properties: First, it is affine equivariant. Second, it is computationally efficient even for large problem sizes. Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method is tested for different contamination models, including recently proposed ones. The method is not only faster than the Fast-MCD method for high dimensional data but also has reasonable accuracy for the tested cases.

关键词： Covariance matrix estimation Robust statistics Outlier detection Optimization semi-definite programming Newton-Raphson method

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Optimized Power Allocation in Nonlinear Sensor Networks via semidefinite programming

Optimized Power Allocation in Nonlinear Sensor Networks via ...

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IEEE 72nd Vehicular Technology Conference Fall 2010

作者： Rashid, Umar Tuan, Hoang Duong Kha, Ha Hoang Univ New S Wales Sch Elect Engg & Telecom Sydney NSW 2052 Australia

ISBN: (纸本)9781424435746

This paper presents an efficient technique for power allocation to the sensor nodes in a nonlinear sensor network (NSN). We minimize mean square error of the estimation of a random scalar parameter subject to a constraint on total amount of power consumed by the sensor nodes. This estimation is carried out at fusion center (FC) which receives the local observations from the sensors located at different positions. We convert the optimization problem into a convex one, and then use semidefinite programming to find the global optimal solution. The simulation results show that our approach outperforms the previous work both for the channel with white noise and the one with colored noise. The proposed strategy also gives better results in case of nonlinear model when compared to the strategy of assigning equal power to sensor nodes.

关键词： Nonlinear sensor network distributed estimation semi-definite programming convex optimization

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