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Unsupervised learning of finite mixture models

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2002年第3期24卷 381-396页

作者： Figueiredo, MAT Jain, AK Inst Super Tecn Inst Telecommun P-1049001 Lisbon Portugal Inst Super Tecn Dept Elect & Comp Engn P-1049001 Lisbon Portugal Michigan State Univ Dept Comp Sci & Engn E Lansing MI 48824 USA

This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective "unsupervised" is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models;instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm;in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach.

关键词： finite mixtures unsupervised learning model selection minimum message length criterion Bayesian methods expectation-maximization algorithm clustering

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A Globally-Variant Locally-Constant Model for Fusion of Labels from Multiple Diverse Experts without Using Reference Labels

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2013年第4期35卷 769-783页

作者： Audhkhasi, Kartik Narayanan, Shrikanth (Shri) Univ So Calif Dept Elect Engn SAIL Los Angeles CA 90089 USA

Researchers have shown that fusion of categorical labels from multiple experts-humans or machine classifiers-improves the accuracy and generalizability of the overall classification system. Simple plurality is a popular technique for performing this fusion, but it gives equal importance to labels from all experts, who may not be equally reliable or consistent across the dataset. Estimation of expert reliability without knowing the reference labels is, however, a challenging problem. Most previous works deal with these challenges by modeling expert reliability as constant over the entire data (feature) space. This paper presents a model based on the consideration that in dealing with real-world data, expert reliability is variable over the complete feature space but constant over local clusters of homogeneous instances. This model jointly learns a classifier and expert reliability parameters without assuming knowledge of the reference labels using the expectation-maximization (EM) algorithm. Classification experiments on simulated data, data from the UCI Machine Learning Repository, and two emotional speech classification datasets show the benefits of the proposed model. Using a metric based on the Jensen-Shannon divergence, we empirically show that the proposed model gives greater benefit for datasets where expert reliability is highly variable over the feature space.

关键词： Multiple diverse experts label fusion label reliability expectation-maximization algorithm human annotation emotion recognition

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Remaining useful life prediction for degrading systems with random shocks considering measurement uncertainty

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JOURNAL OF MANUFACTURING SYSTEMS 2021年 61卷 782-798页

作者： Kong, Xuefeng Yang, Jun Li, Lei Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China

Degradation data have been widely used for the remaining useful life (RUL) prediction of systems. Most existing works apply a preset model to capture the degradation process and focus on the degradation process without shocks or constant shock effects. More generally, the actual degradation path is unobservable due to the existence of measurement uncertainty, which interferes with the determination of the degradation model. Besides, the effect of random shocks is usually fluctuating. Given these problems, a general degradation model with the random shock fluctuant effects considering the measurement uncertainty is first developed to describe the degradation process, and a two-step approach combining the arithmetic average filter and the Bayesian information criterion is adopted to identify the degradation path. Subsequently, the transfer processes of the actual degradation state and the abrupt change caused by shocks are depicted using a two-dimensional state-space model, and an expectation-maximization algorithm combined with the particle filtering is developed for parameter estimation. Furthermore, the explicit solution of RUL distribution is obtained when only considering harmful shocks, while a simulation method of RUL distribution is provided when both harmful and beneficial shocks exist. Finally, the effectiveness of the proposed method is verified by a numerical example and two practical case studies.

关键词： Remaining useful life Degradation process Measurement uncertainty Random shock effects expectation-maximization algorithm

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Identifying driver heterogeneity in car-following based on a random coefficient model

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2013年 36卷 35-44页

作者： Kim, Ikki Kim, Taewan Sohn, Keemin Hanyang Univ Dept Transportat & Logist Engn Ansan Gyunggi Do South Korea Chung Ang Univ Dept Urban Engn Seoul 156756 South Korea

As computing capabilities have advanced, random coefficient models have emerged as the mainstream method of dealing with traveler behaviors in transport studies. Car-following models with random coefficients, however, are rarely used, although many kinds of car-following models have been attempted. For the present study, we proposed a rigorous methodology to calibrate a GM-type car-following model with random coefficients, which could account for the heterogeneity across drivers who respond differently to stimuli. To avert both the curse of dimensionality and the lack of empirical identification, which can be a part of dealing with a simulated likelihood, a robust algorithm called the expectation-maximization (EM) was adopted. The calibration results confirmed that random coefficients of the model fluctuated considerably across drivers, and were correlated with each other. The exclusion of these facts might be a potential reason for the difficulty in simulating real traffic situations based on a single car-following model with constant coefficients.

关键词： Car-following model Random coefficient Heterogeneity expectation-maximization algorithm Maximum simulated likelihood

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ANDERSON ACCELERATION FOR FIXED-POINT ITERATIONS

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2011年第4期49卷 1715-1735页

作者： Walker, Homer F. Ni, Peng Worcester Polytech Inst Dept Math Sci Worcester MA 01609 USA

This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [J. Assoc. Comput. Mach., 12 (1965), pp. 547-560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anderson mixing;however, it seems to have been untried or underexploited in many other important applications. Moreover, while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities, this method has received relatively little attention from these communities over the years. A recent paper by H. Fang and Y. Saad [Numer. Linear Algebra Appl., 16 (2009), pp. 197-221] has clarified a remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended it to define a broader Anderson family of acceleration methods. In this paper, our goals are to shed additional light on Anderson acceleration and to draw further attention to its usefulness as a general tool. We first show that, on linear problems, Anderson acceleration without truncation is "essentially equivalent" in a certain sense to the generalized minimal residual (GMRES) method. We also show that the Type 1 variant in the Fang-Saad Anderson family is similarly essentially equivalent to the Arnoldi (full orthogonalization) method. We then discuss practical considerations for implementing Anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications.

关键词： acceleration methods fixed-point iterations generalized minimal residual method Arnoldi (full orthogonalization) method iterative methods expectation-maximization algorithm mixture densities alternating least-squares nonnegative matrix factorization domain decomposition

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Infer Metagenomic Abundance and Reveal Homologous Genomes Based on the Structure of Taxonomy Tree

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2015年第5期12卷 1112-1122页

作者： Qiu, Yu-Qing Tian, Xue Zhang, Shihua Chinese Acad Sci Natl Ctr Math & Interdisciplinary Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Hangzhou Dianzi Univ Sch Sci Hangzhou 310018 Zhejiang Peoples R China

Metagenomic research uses sequencing technologies to investigate the genetic biodiversity of microbiomes presented in various ecosystems or animal tissues. The composition of a microbial community is highly associated with the environment in which the organisms exist. As large amount of sequencing short reads of microorganism genomes obtained, accurately estimating the abundance of microorganisms within a metagenomic sample is becoming an increasing challenge in bioinformatics. In this paper, we describe a hierarchical taxonomy tree-based mixture model (HTTMM) for estimating the abundance of taxon within a microbial community by incorporating the structure of the taxonomy tree. In this model, genome-specific short reads and homologous short reads among genomes can be distinguished and represented by leaf and intermediate nodes in the taxonomy tree, respectively. We adopt an expectation-maximization algorithm to solve this model. Using simulated and real-world data, we demonstrate that the proposed method is superior to both flat mixture model and lowest common ancestry-based methods. Moreover, this model can reveal previously unaddressed homologous genomes.

关键词： Metagenomics abundance estimation taxonomy tree expectation-maximization algorithm

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Doubly Stochastic Cumulative Damage Model for RUL Prediction of HDDs in Uncertain Operating Environments

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2021年第9期68卷 8743-8752页

作者： Peng, Yizhen Wang, Yu Wang, Guochao Tsui, Kwok-Leung Chongqing Univ State Key Lab Mech Transmiss Coll Mech Engn Chongqing 400044 Peoples R China Xi An Jiao Tong Univ Sch Mech Engn State Key Lab Mfg & Syst Engn Xian 710049 Peoples R China Zhejiang Univ Technol Key Lab E&M Hangzhou 310023 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

Degradation modeling and remaining useful life (RUL) prediction for hard disk drives are crucial for exploring the failure mechanism, evaluating the design reliability and improving the design. Motivated by the fact that magnetic head degradation is the most prevailing failure mode, a variety of methods for head degradation problem have been proposed. For example, non-homogeneous Poisson processes were developed to deal with such problems. However, a general non-homogeneous Poisson process assumes that the mean cumulative function is deterministic. This assumption cannot be satisfied when the degradation process contains stochastic dynamics in uncertain operating environments. To solve this problem, this article proposes a non-homogeneous Poisson process with a stochastic mean cumulative function that uses Gaussian noise terms to capture the stochastic effects. Then, a nonlinear state-space model is built using the proposed model to track the dynamic degradation process and predict the RUL of magnetic head under uncertain operating conditions. To estimate and update the model parameters adaptively, a stochastic filter and a maximum likelihood estimation (smoother) based on the expectation-maximization algorithm is derived. Finally, a real case study is used to illustrate the effectiveness of the proposed method.

关键词： Degradation Magnetic heads Stochastic processes Electric shock Adaptation models Predictive models Reliability Degradation modeling expectation-maximization algorithm nonhomogeneous Poisson process nonlinear filter and smoother state-space model

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Nonparametric Method for Modeling Clustering Phenomena in Emergency Calls Under Spatial-Temporal Self-Exciting Point Processes

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IEEE ACCESS 2019年 7卷 24865-24876页

作者： Li, Chenlong Song, Zhanjie Wang, Xu Tianjin Univ Sch Math Tianjin 300350 Peoples R China Wilfrid Laurier Univ Dept Math Waterloo ON N2L 3C5 Canada Tianjin Univ Visual Pattern Anal Res Lab Tianjin 300072 Peoples R China

In this paper, a nonparametric spatial-temporal self-exciting point process is proposed to model clustering features in emergency calls. Gaussian kernel density functions are considered. The expectation-maximization algorithm is adopted for estimating the model. A simulation study is designed to carefully examine the performance of the proposed nonparametric method. The spatial-temporal patterns of the emergency calls in Montgomery County of Pennsylvania are studied using the proposed nonparametric model. The results demonstrate that the proposed nonparametric model captures the clustering phenomena present in the emergency calls from Montgomery County very well. Further, the proposed parameter estimation method results in robust and precise estimates.

关键词： Spatial-temporal point processes emergency calls nonparametric model maximum likelihood estimation expectation-maximization algorithm

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Image thresholding based on the EM algorithm and the generalized Gaussian distribution

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PATTERN RECOGNITION 2007年第2期40卷 619-634页

作者： Bazi, Yakoub Bruzzone, Lorenzo Melgani, Farid Univ Trent Dept Informat & Commun Technol I-38050 Trento Italy

In this paper. a novel parametric and global image histogram thresholding method is presented. It is based on the estimation of the statistical parameters of "object" and "background" classes by the expectation-maximization (EM) algorithm, under the assumption that these two classes follow a generalized Gaussian (GG) distribution. The adoption of such a statistical model as an alternative to the more common Gaussian model is motivated by its attractive capability to approximate a broad variety of statistical behaviors with a small number of parameters. Since the quality of the solution provided by the iterative EM algorithm is strongly affected by initial conditions (which. if inappropriately set, may lead to unreliable estimation), a robust initialization strategy based on genetic algorithms (GAs) is proposed. Experimental results obtained on simulated and real images confirm the effectiveness of the proposed method. (c) 2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： image thresholding expectation-maximization algorithm generalized Gaussian distribution genetic algorithms

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Parameter identification of nonlinear multirate time-delay system with uncertain output delays

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2018年第12期40卷 3498-3506页

作者： Yang, Xianqiang Xiong, Weili Wang, Zeyuan Liu, Xin Harbin Inst Technol Harbin Heilongjiang Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi Peoples R China

The joint parameter and time-delay estimation problems for a class of nonlinear multirate time-delay system with uncertain output delays are addressed in this paper. The practical process typically has time-delay properties and the process data are often multirate, sampled with output data inevitably corrupted by uncertain delays. The linear parameter varying (LPV) finite impulse response (FIR) multirate time-delay model is initially built to describe the considered system. The problems of over-parameterization and the existence of both continuous model parameters and discrete time-delays have made the conventional maximum likelihood difficult to solve the considered problems. In order to handle these problems, the joint parameter and time-delay estimation for the LPV FIR multirate time-delay model are formulated in the expectation-maximization scheme, and the algorithm to estimate the model parameters and time-delays is derived, simultaneously based on multirate process data. The efficacy of the proposed method is verified through a numerical simulation and a practical chemical plant.

关键词： System identification nonlinear time-delay model multirate data the continuous stirred tank reactor system expectation-maximization algorithm

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