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Maximum smoothed likelihood component density estimation in mixture models with known mixing proportions

ELECTRONIC JOURNAL OF STATISTICS 2019年第2期13卷 4035-4078页

作者： Yu, Tao Li, Pengfei Qin, Jing Natl Univ Singapore Dept Stat & Appl Probabil Singapore 117546 Singapore Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada NIAID NIH 9000 Rockville Pike Bethesda MD 20892 USA

Mixture models appear in many research areas. In genetic and epidemiology applications, sometimes the mixture proportions may vary but are known. For such data, the existing methods for the underlying component density estimation may produce undesirable results: negative values in the density estimates. In this paper, we propose a maximum smoothed likelihood method to estimate these component density functions. The proposed estimates maximize a smoothed log likelihood function which can inherit all the important properties of probability density functions. A majorization-minimization algorithm is suggested to compute the proposed estimates numerically. We show that, starting from any initial value, the algorithm converges. Furthermore, we establish the asymptotic convergence rate of the L-1 errors of our proposed estimators. Our method provides a general framework for dealing with many similar mixture model problems. An adaptive procedure is suggested for choosing the bandwidths in our estimation procedure. Simulation studies show that the proposed method is very promising and can be much more efficient than the existing method in terms of the L-1 errors. A malaria data application shows the advantages of our method over others.

关键词： EM-like algorithm empirical process M-estimators majorization-minimization algorithm mixture data smoothed like-lihood function

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Laplace Nonnegative Matrix Factorization with Application to Semi-supervised Audio Denoising 27

Laplace Nonnegative Matrix Factorization with Application to...

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27th European Signal Processing Conference (EUSIPCO)

作者： Tanji, Hiroki Murakami, Takahiro Kamata, Hiroyuki Meiji Univ Dept Elect & Bioinformat Sch Sci & Technol Tokyo Japan Univ Surrey Ctr Vis Speech & Signal Proc CVSSP Guildford Surrey England

ISBN: (纸本)9789082797039

This paper proposes two statistical models for the nonnegative matrix factorization (NMF) based on heavy-tailed distributions. In the NMF for acoustic signals, previous works justify the additivity of an observed spectrogram using the reproductive property of a probability density function. However, the effectiveness of these properties is not clear. Consequently, to construct a model robust to noise, statistical models based on heavy-tailed distributions are recently growing up. In this paper, as heavy-tailed models for the NMF, we introduce statistical models based on the complex Laplace distributions, and call them Laplace-NMF. Moreover, we derive convergence-guaranteed optimization algorithms to estimate parameters. From our formulation, a statistical interpretation of the Itakura-Saito (IS) divergence-based NMF is newly revealed. We confirm the effectiveness of Laplace-NMF in semi-supervised audio denoising.

关键词： complex Laplace distribution nonnegative matrix factorization majorization-minimization algorithm source separation

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Signal subspace change detection in structured covariance matrices 27

Signal subspace change detection in structured covariance ma...

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27th European Signal Processing Conference (EUSIPCO)

作者： Ben Abdallah, R. Breloy, A. Taylor, A. El Korso, M. N. Lautru, D. Univ Paris Nanterre IUT Ville dAvray LEME EA 4416 Paris France Univ Paris Saclay ONERA DEMR F-91123 Palaiseau France

ISBN: (纸本)9789082797039

Testing common properties between covariance matrices is a relevant approach in a plethora of applications. In this paper, we derive a new statistical test in the context of structured covariance matrices. Specifically, we consider low rank signal component plus white Gaussian noise structure. Our aim is to test the equality of the principal subspace, i.e., subspace spanned by the principal eigenvectors of a group of covariance matrices. A decision statistic is derived using the generalized likelihood ratio test. As the formulation of the proposed test implies a non-trivial optimization problem, we derive an appropriate majorization-minimization algorithm. Finally, numerical simulations illustrate the properties of the newly proposed detector compared to the state of the art.

关键词： Generalized likelihood ratio test subspace testing low rank structure majorization-minimization algorithm

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Nonnegative Matrix Factorization With Basis Clustering Using Cepstral Distance Regularization

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2018年第6期26卷 1025-1036页

作者： Kameoka, Hirokazu Higuchi, Takuya Tanaka, Mikihiro Li, Li NTT Corp NTT Commun Sci Labs Tokyo 2430198 Japan Univ Tokyo Tokyo 1138656 Japan Univ Tsukuba Tsukuba Ibaraki 3058577 Japan

One successful approach for audio source separation involves applying nonnegative matrix factorization (NMF) to a magnitude spectrogram regarded as a nonnegative matrix. This can be interpreted as approximating the observed spectra at each time frame as the linear sum of the basis spectra scaled by time-varying amplitudes. This paper deals with the problem of the unsupervised instrument-wise source separation of polyphonic signals based on an extension of the NMF approach. We focus on the fact that each piece of music is typically played on a handful of musical instruments, which allows us to assume that the spectra of the underlying audio events in a polyphonic signal can be grouped into a reasonably small number of clusters in the mel-frequency cepstral coefficient (MFCC) domain. Based on this assumption, we propose formulating factorization of amagnitude spectrogram and clustering of the basis spectra in the MFCC domain as a joint optimization problem and derive a novel optimization algorithm based on the majorization-minimization principle. Experimental results revealed that our method was superior to a two-stage algorithm that consists of performing factorization followed by clustering the basis spectra, thus showing the advantage of the joint optimization approach.

关键词： Audio source separation nonnegative matrix factorization (NMF) basis clustering mel-frequency cepstral coefficient (MFCC) majorization-minimization algorithm

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Sparse Bayesian Approach for DOD and DOA Estimation With Bistatic MIMO Radar

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IEEE ACCESS 2019年 7卷 155335-155346页

作者： Cao, Zheng Zhou, Lei Dai, Jisheng Jiangsu Univ Dept Elect Engn Zhenjiang 212013 Jiangsu Peoples R China

This study addresses the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation with bistatic multiple-input multiple-output (MIMO) radar. To the best of our knowledge, a limited number of sparse Bayesian learning (SBL)-based methods exist that can be applied to joint DOD and DOA estimation. This is because of the heavy computational load and strong correlation between the nearby basis. To overcome these challenges, we present a new coarse non-uniformly sampled 2D grid and propose an improved SBL-based method for joint estimation of the DOD and DOA in MIMO radar. With the new grid, the computational load can be significantly reduced, and the nearby 2D grid points can provide a low correlation basis. To handle the modeling error derived from the coarse grid, we also introduce a modified linear approximation method into the SBL framework in which the locations of grid points are considered as adjustable parameters, and the grid points can be updated recursively. Finally, a block majorization-minimization algorithm is applied to perform Bayesian inference. Experimental results indicate that our method can improve the joint DOD and DOA estimation performance, particularly in the case of low signal-noise-ratio, limited snapshots, or correlated signals.

关键词： DOD and DOA estimation bistatic MIMO radar sparse Bayesian learning majorization-minimization algorithm coarse non-uniformly sampled 2D grid

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majorization-minimization generalized Krylov subspace methods for - optimization applied to image restoration

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BIT NUMERICAL MATHEMATICS 2017年第2期57卷 351-378页

作者： Huang, G. Lanza, A. Morigi, S. Reichel, L. Sgallari, F. Chengdu Univ Technol Coll Management Sci Geomath Key Lab Sichuan Chengdu 610059 Peoples R China Univ Bologna Dept Math Bologna Italy Kent State Univ Dept Math Sci Kent OH 44242 USA

A new majorization-minimization framework for - image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized - functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed.

关键词： l(p)-l(q) minimization Generalized Krylov subspace majorization-minimization algorithm Image restoration

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Fast Domain Decomposition for Global Image Smoothing

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第8期26卷 4079-4091页

作者： Kim, Youngjung Min, Dongbo Ham, Bumsub Sohn, Kwanghoon Yonsei Univ Sch Elect & Elect Engn Seoul 120749 South Korea Chungnam Natl Univ Sch Comp Sci & Engn Taejon 305764 South Korea

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and regularization terms. At the price of high-computational cost, this global EPS approach is more robust and versatile than a local one that typically has a form of weighted averaging. In this paper, we introduce an efficient decomposition-based method for global EPS that minimizes the objective function of L-2 data and (possibly non-smooth and non-convex) regularization terms in linear time. Different from previous decomposition-based methods, which require solving a large linear system, our approach solves an equivalent constrained optimization problem, resulting in a sequence of 1-D sub-problems. This enables applying fast linear time solver for weighted-least squares and -L-1 smoothing problems. An alternating direction method of multipliers algorithm is adopted to guarantee fast convergence. Our method is fully parallelizable, and its runtime is even comparable to the state-of-the-art local EPS approaches. We also propose a family of fast majorization-minimization algorithms that minimize an objective with non-convex regularization terms. Experimental results demonstrate the effectiveness and flexibility of our approach in a range of image processing and computational photography applications.

关键词： Edge-preserving image smoothing joint image filtering weighted-least squares alternating minimization majorization-minimization algorithm

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Compressive Sensing Reconstruction Based on Weighted Directional Total Variation

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Journal of Shanghai Jiaotong university(Science) 2017年第1期22卷 114-120页

作者：闵莉花冯灿 School of Science Nanjing University of Posts and Telecommunications Department of Beidou North Information Control Research Academy Group Co.Ltd.

Directionality of image plays a very important role in human visual system and it is important prior information of image. In this paper we propose a weighted directional total variation model to reconstruct image from its finite number of noisy compressive samples. A novel self-adaption, texture preservation method is designed to select the weight. Inspired by majorization-minimization scheme, we develop an efficient algorithm to seek the optimal solution of the proposed model by minimizing a sequence of quadratic surrogate penalties. The numerical examples are performed to compare its performance with four state-of-the-art algorithms. Experimental results clearly show that our method has better reconstruction accuracy on texture images than the existing scheme.

关键词： compressive sensing weighted directional total variation majorization-minimization algorithm TP 391.4 A

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Two-mode three-way dominance points model for periodic dissimilarity 5

Two-mode three-way dominance points model for periodic dissi...

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5th International Conference on Applied Computing and Information Technology, 2017 4th International Conference on Computational Science/Intelligence and Applied Informatics and 2017 1st International Conference on Big Data, Cloud Computing, Data Science and Engineering, ACIT-CSII-BCD 2017

作者： Tsuchida, Jun Yadohisa, Hiroshi Graduate School of Culture and Information Science Doshisha Univesity Kyoto Japan Department of Culture and Information Science Doshisha Univesity Kyoto Japan

ISBN: (纸本)9781538633021

Asymmetric multidimensional scaling (AMDS) is important for visualizing asymmetric relationships between objects. The dominance point model involves AMDS and represents asymmetry between objects through the difference in the distances between the dominance point and objects. The advantage of this model is that the dominance point and points of objects are represented in the same space. However, there is a problem when applying the dominance point to a two-mode three-way distance model (object X object X condition). The dominance point model ignores the order of condition;that is, the estimator of the model is not changed although the order of condition is changed. To overcome this problem, we propose a two-mode three-way dominance point model using a hypersphere. Constraining the coordinate vector of objects on the hypersphere, the proposed model considers the order of condition. Moreover, the coordinate vector of objects has a periodic property. We introduce the majorizing function of the objective function of our model and obtain the estimator using the majorization-minimization algorithm. © 2017 IEEE.

关键词： Asymmetric model majorization-minimization algorithm Multidimensional scaling

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Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods

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JOURNAL OF BIOMEDICAL OPTICS 2016年第1期21卷 1-10页

作者： Zhu, Dianwen Li, Changqing Univ Calif Merced Sch Engn 5200 N Lake Rd Merced CA 95343 USA

Fluorescence molecular tomography (FMT) is a significant preclinical imaging modality that has been actively studied in the past two decades. It remains a challenging task to obtain fast and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden and the ill-posed nature of the inverse problem. We have recently studied a nonuniform multiplicative updating algorithm that combines with the ordered subsets (OS) method for fast convergence. However, increasing the number of OS leads to greater approximation errors and the speed gain from larger number of OS is limited. We propose to further enhance the convergence speed by incorporating a first-order momentum method that uses previous iterations to achieve optimal convergence rate. Using numerical simulations and a cubic phantom experiment, we have systematically compared the effects of the momentum technique, the OS method, and the nonuniform updating scheme in accelerating the FMT reconstruction. We found that the proposed combined method can produce a high-quality image using an order of magnitude less time. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： fluorescence molecular tomography iterative image reconstruction ordered subsets momentum nonuniform update majorization-minimization algorithm

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