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Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.


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Journal ArticleDOI
TL;DR: Two stochastic algorithms are derived from this general Classification EM algorithm, incorporating random perturbations, to reduce the initial-position dependence of the classical optimization clustering algorithms.

810 citations

Journal ArticleDOI
TL;DR: In this article, a mathematical model tailored to the physics of positron emissions is presented, and the model is used to describe the image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data.
Abstract: Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the physics of positron emissions, and we use the model to describe the basic image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data. We describe various estimation procedures, such as the maximum likelihood (ML) method (using the EM algorithm), the method of moments, and the least squares method. A computer simulation of a PET experiment is then used to demonstrate the ML and the least squares reconstructions. The main purposes of this article are to report on what we believe is an...

804 citations

Journal ArticleDOI
Y. Vardi1
TL;DR: In this article, the problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between a pair of vertices, determined according to a known Markov chain fixed for that pair).
Abstract: The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between each directed pair of nodes, determined according to a known Markov chain fixed for that pair). Maximum likelihood estimation and related approximations are discussed, and computational difficulties are pointed out. A detailed methodology is presented for estimates based on the method of moments. The estimates are derived algorithmically, taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an EM algorithm, resulting in a particularly simple solution to a hard problem. A small simulation study is carried out.

801 citations

Journal ArticleDOI
TL;DR: The stochastic approximation EM (SAEM), which replaces the expectation step of the EM algorithm by one iteration of a stochastics approximation procedure, is introduced and it is proved that, under mild additional conditions, the attractive stationary points of the SAEM algorithm correspond to the local maxima of the function.
Abstract: The expectation-maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations, however, this method is not applicable because the expectation step cannot be performed in closed form. To deal with these problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the expectation step of the EM algorithm by one iteration of a stochastic approximation procedure. The convergence of the SAEM algorithm is established under conditions that are applicable to many practical situations. Moreover, it is proved that, under mild additional conditions, the attractive stationary points of the SAEM algorithm correspond to the local maxima of the function. presented to support our findings.

795 citations

Journal ArticleDOI
TL;DR: This paper fits Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered.
Abstract: Fisher-Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered. Low dimensional views are an important by-product of LDA-our new techniques inherit this feature. We can control the within-class spread of the subclass centres relative to the between-class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA.

791 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023114
2022245
2021438
2020410
2019484
2018519