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88th IEEE Vehicular Technology Conference (VTC-Fall)

作者： Zhang, Fan Wu, Qiong Wang, Hao Shi, Yuanming ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China

ISBN: (纸本)9781538663585

In this paper, we propose a novel reformulation of the Mixed Integer Programming (MIP) problem for solving the Cloud Radio Access Network (Cloud-RAN) power consumption minimization problem, and present an l(2)-box technique to reformulate the MIP problem into an exact and continuous model for recasting the binary constraints into a box with an l(2) sphere constraint. A majorization-minimization (MM) dual ascent algorithm is proposed for solving the reformulated problem, which leads to solving a sequence of Difference of Convex (DC) subproblems handled by an inexact MM algorithm. After obtaining the final solution, we use it as the initial result of the bi-section Group Sparse Beamforming (GSBF) algorithm to promote the group-sparsity of beamformers, rather than using the weighted l(1)/l(2)-norm. Simulation results indicate that the new method outperforms the bi-section GSBF algorithm in achieving smaller network power consumption, especially in sparser cases, i.e., Cloud-RANs with a lot of Remote Radio Heads (RRHs) but fewer users.

关键词： Cloud-RAN l(2)-box difference of convex problems majorization-minimization algorithms dual ascent methods inexact algorithms group-sparsity

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Structured variable selection via prior-induced hierarchical penalty functions

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 96卷 87-103页

作者： Yen, Tso-Jung Yen, Yu-Min Acad Sinica Inst Stat Sci 128 Acad RdSect 2 Taipei 11529 Taiwan Natl Chengchi Univ Dept Int Business 64Sect 2Zhi Nan Rd Taipei 11605 Taiwan

The paper studies a grouped variable selection problem in a linear regression setting by proposing a hierarchical penalty function to model collective behavior of the regression coefficients. This hierarchical penalty function consists of two levels. At the top level, it models the group effect of covariates by introducing an index function on the event that the l(2)-norm of the corresponding regression coefficients is not equal to zero. At the bottom level, it models the individual effect of a covariate with an index function on the event that the corresponding regression coefficient is not equal to zero. Under this hierarchical penalty function, model estimation can be conducted by applying an iteration-based numerical procedure to solve a sequence of modified optimization problems. Simulation study shows that the proposed estimator performs relatively well when the number of covariates exceeds the sample size, and when both the true and false covariates are included in the same group. Theoretical analysis suggests that the l(2) estimation error of the proposed estimator can achieve a good upper bound if some regularity conditions are satisfied. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Group sparsity Spike and slab priors Log-sum approximation to the l(0)-norm majorization-minimization algorithms Alternating direction method of multipliers

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ON TENSORS, SPARSITY, AND NONNEGATIVE FACTORIZATIONS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2012年第4期33卷 1272-1299页

作者： Chi, Eric C. Kolda, Tamara G. Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA Sandia Natl Labs Livermore CA USA

Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative log-likelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP-PARAFAC alternating Poisson regression (CP-APR) that is based on a majorization-minimization approach. It can be shown that CP-APR is a generalization of the Lee-Seung multiplicative updates. We show how to prevent the algorithm from converging to non-KKT points and prove convergence of CP-APR under mild conditions. We also explain how to implement CP-APR for large-scale sparse tensors and present results on several data sets, both real and simulated.

关键词： nonnegative tensor factorization nonnegative CANDECOMP-PARAFAC Poisson tensor factorization Lee-Seung multiplicative updates majorization-minimization algorithms

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A majorization-minimization APPROACH TO VARIABLE SELECTION USING SPIKE AND SLAB PRIORS

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ANNALS OF STATISTICS 2011年第3期39卷 1748-1775页

作者： Yen, Tso-Jung Acad Sinica Inst Stat Sci Taipei 115 Taiwan

We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a Lagrangian form in that regression coefficients are regularized by a mixture of squared l(2) and l(0) norms. A tight approximation to the l(0) norm using majorization minimization techniques is derived, and a coordinate descent algorithm in conjunction with a soft-thresholding scheme is used in searching for the optimizer of the approximate objective. Simulation studies show that the proposed method can lead to more accurate variable selection than other benchmark methods. Theoretical results show that under regular conditions, sign consistency can be established, even when the Irrepresentable Condition is violated. Results on posterior model consistency and estimation consistency, and an extension to parameter estimation in the generalized linear models are provided.

关键词： MAP estimation l(0) norm majorization-minimization algorithms Irrepresentable Condition

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A total variation denoising algorithm for hyperspectral data

A total variation denoising algorithm for hyperspectral data

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Conference on Infrared, Millimeter Wave, and Terahertz Technologies

作者： Li Ting Chen Xiao-mei Xue Bo Li Qian-qian Ni Guo-qiang Beijing Inst Technol Sch Optoelect Beijing 100081 Peoples R China

ISBN: (纸本)9780819483843

Since noise can undermine the effectiveness of information extracted from hyperspectral imagery, noise reduction is a prerequisite for many classification-based applications of hyperspectral imagery. In this paper, an effective three dimensional total variation denoising algorithm for hyperspectral imagery is introduced. First, a three dimensional objective function of total variation denoising model is derived from the classical two dimensional TV algorithms. For the consideration of the fact that the noise of hyperspectral imagery shows different characteristics in spatial and spectral domain, the objective function is further improved by utilizing two terms (spatial term and spectral term) and separate regularization parameters respectively which can adjust the trade-off between the two terms. Then, the improved objective function is discretized by approximating gradients with local differences, optimized by a quadratic convex function and finally solved by a majorization-minimization based iteration algorithm. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in a desert-dominated area in 2007. Experimental results show that, properly choosing the values of parameters, the new approach removes the indention and restores the spectral absorption peaks more effectively while having a similar improvement of signal-to-noise-ratio as minimum noise fraction (MNF) method.

关键词： Hyperspectral imagery noise reduction total variation majorization-minimization algorithms

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A total variation denoising algorithm for hyperspectral data

A total variation denoising algorithm for hyperspectral data

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2010亚洲光电子会议红外、毫米波和太赫兹技术分会场

作者： LI Ting~(a,b),CHEN Xiao-mei~(*a,b),XUE Bo~(a,b),LI Qian-qian ~(a,b),NI Guo-qiang~(a,b) a School of Optoelectronics,Beijing Institute of Technology,Beijing 100081,P.R.China b Key Laboratory of Photoelectronic Imaging Technology and System(Beijing Institute of Technology),Ministry of Education of China

Since noise can undermine the effectiveness of information extracted from hyperspectral imagery,noise reduction is a prerequisite for many classification-based applications of hyperspectral *** this paper,an effective three dimensional total variation denoising algorithm for hyperspectral imagery is ***,a three dimensional objective function of total variation denoising model is derived from the classical two dimensional TV *** the consideration of the fact that the noise of hyperspectral imagery shows different characteristics in spatial and spectral domain,the objective function is further improved by utilizing two terms(spatial term and spectral term) and separate regularization parameters respectively which can adjust the trade-off between the two ***,the improved objective function is discretized by approximating gradients with local differences,optimized by a quadratic convex function and finally solved by a majorization-minimization based iteration *** performance of the new algorithm is experimented on a set of Hyperion imageries acquired in a desert-dominated area in *** results show that,properly choosing the values of parameters,the new approach removes the indention and restores the spectral absorption peaks more effectively while having a similar improvement of signal-to-noise-ratio as minimum noise fraction(MNF) method.

关键词： Hyperspectral imagery noise reduction total variation majorization-minimization algorithms

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On total variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavalet denoising

On total variation denoising: A new majorization-minimizatio...

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IEEE International Conference on Image Processing (ICIP 2006)

作者： Figueiredo, M. A. T. Dias, J. B. Oliveira, J. P. Nowak, R. D. Univ Tecn Lisboa Inst Telecommun Inst Super Tecn P-1049 Lisbon Portugal Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA

ISBN: (纸本)9781424404810

Image denoising is a classical problem which has been addressed using a variety of conceptual frameworks and computational tools. Most approaches use some form of penalty/prior as a regularizer, expressing a preference for images with some form of (generalized) "smoothness". Total variation (TV) and wavelet-based methods have received a great deal of attention in the last decade and are among the state of the art in this problem. However, as far as we know, no experimental studies have been carried out, comparing the relative performance of the two classes of methods. In this paper, we present the results of such a comparison. Prior to that, we introduce a new majorization-minimization algorithm to implement the TV denoising criterion. We conclude that TV is outperformed by recent state of the art wavelet-based denoising methods, but performs competitively with older wavelet-based methods.

关键词： image restoration total variation image denoising majorization-minimization algorithms

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