Topic
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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TL;DR: A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach and removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model.
Abstract: A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.
92 citations
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TL;DR: A stochastic approximation procedure is used to recursively estimate the parameters of the Gaussian mixture model, and to simultaneously obtain the asymptotically optimal number of the mixture components.
92 citations
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TL;DR: A stochastic version of RPCL and its type A variant, respectively, are proposed, in which the difficult selection problem of delearning rate has been novelly circumvented.
Abstract: Expectation-maximization (EM) algorithm (A.P. Dempster et al., 1977) has been extensively used in density mixture clustering problems, but it is unable to-perform model selection automatically. This paper, therefore, proposes to learn the model parameters via maximizing a weighted likelihood. Under a specific weight design, we give out a rival penalized expectation-maximization (RPEM) algorithm, which makes the components in a density mixture compete each other at each time step. Not only are the associated parameters of the winner updated to adapt to an input, but also all rivals' parameters are penalized with the strength proportional to the corresponding posterior density probabilities. Compared to the EM algorithm (A.P. Dempster et al., 1977), the RPEM is able to fade out the redundant densities from a density mixture during the learning process. Hence, it can automatically select an appropriate number of densities in density mixture clustering. We experimentally demonstrate its outstanding performance on Gaussian mixtures and color image segmentation problem. Moreover, a simplified version of RPEM generalizes our recently proposed RPCCL algorithm (Y.M. Cheung, 2002) so that it is applicable to elliptical clusters as well with any input proportion. Compared to the existing heuristic RPCL (L. Xu et al., 1993) and its variants, this generalized RPCCL (G-RPCCL) circumvents the difficult preselection of the so-called delearning rate. Additionally, a special setting of the G-RPCCL not only degenerates to RPCL and its Type A variant, but also gives a guidance to choose an appropriate delearning rate for them. Subsequently, we propose a stochastic version of RPCL and its type A variant, respectively, in which the difficult selection problem of delearning rate has been novelly circumvented. The experiments show the promising results of this stochastic implementation.
91 citations
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TL;DR: A new Bayesian model is proposed for image segmentation based upon Gaussian mixture models (GMM) with spatial smoothness constraints that exploits the Dirichlet compound multinomial (DCM) probability density and a Gauss-Markov random field on theDirichlet parameters to impose smoothness.
Abstract: A new Bayesian model is proposed for image segmentation based upon Gaussian mixture models (GMM) with spatial smoothness constraints. This model exploits the Dirichlet compound multinomial (DCM) probability density to model the mixing proportions (i.e., the probabilities of class labels) and a Gauss-Markov random field (MRF) on the Dirichlet parameters to impose smoothness. The main advantages of this model are two. First, it explicitly models the mixing proportions as probability vectors and simultaneously imposes spatial smoothness. Second, it results in closed form parameter updates using a maximum a posteriori (MAP) expectation-maximization (EM) algorithm. Previous efforts on this problem used models that did not model the mixing proportions explicitly as probability vectors or could not be solved exactly requiring either time consuming Markov Chain Monte Carlo (MCMC) or inexact variational approximation methods. Numerical experiments are presented that demonstrate the superiority of the proposed model for image segmentation compared to other GMM-based approaches. The model is also successfully compared to state of the art image segmentation methods in clustering both natural images and images degraded by noise.
91 citations
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TL;DR: A new model is proposed for Microarray‐CGH (comparative genomic hybridization) experiments, combining a segmentation model with a mixture model, and a new hybrid algorithm called dynamic programming–expectation maximization (DP–EM) is presented to estimate the parameters of the model by maximum likelihood.
Abstract: Microarray-CGH (comparative genomic hybridization) experiments are used to detect and map chromosomal imbalances. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose representative sequences share the same relative copy number on average. Segmentation methods constitute a natural framework for the analysis, but they do not provide a biological status for the detected segments. We propose a new model for this segmentation/clustering problem, combining a segmentation model with a mixture model. We present a new hybrid algorithm called dynamic programming-expectation maximization (DP-EM) to estimate the parameters of the model by maximum likelihood. This algorithm combines DP and the EM algorithm. We also propose a model selection heuristic to select the number of clusters and the number of segments. An example of our procedure is presented, based on publicly available data sets. We compare our method to segmentation methods and to hidden Markov models, and we show that the new segmentation/clustering model is a promising alternative that can be applied in the more general context of signal processing.
91 citations