The EM Algorithm and Extensions.

Gentle, James E.; McLachlan, G. J.; Krishnan, T.

doi:10.2307/2534032

Cited by 25 publications

(9 citation statements)

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“…The most common method of estimating the parameters of a mixture model is the Expectation Maximization (EM) Algorithm (Dempster et al 1977;McLachlan & Krishnan 2008), which is an iterative method for finding maximum likelihood estimates (MLEs) in incomplete data scenarios. Andrews & McNicholas (2012) used a variant of EM known as the Expectation Conditional Maximization (ECM) algorithm (Meng & Rubin 1993) to estimate the parameters of the tMM.…”

Section: Mbc With T-mixturesmentioning

confidence: 99%

Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Chattopadhyay

Maitra

2018

Monthly Notices of the Royal Astronomical Society

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Section: Mbc With T-mixturesmentioning

confidence: 99%

Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Chattopadhyay

Maitra

2018

Monthly Notices of the Royal Astronomical Society

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“…The most commonly-used mixture model is the Gaussian mixture model (GMM), where each f k (x; ν k ) is taken to be the multivariate Gaussian density φ(x; µ k , Σ k ) with mean µ k and dispersion matrix Σ k . Estimation is via the Expectation-Maximization (EM) algorithm Dempster et al (1977); McLachlan & Krishnan (2008) which has the following steps:…”

Section: Model-based Clusteringmentioning

confidence: 99%

Gaussian-mixture-model-based cluster analysis finds five kinds of gamma-ray bursts in the BATSE catalogue

Chattopadhyay

Maitra

2017

Monthly Notices of the Royal Astronomical Society

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Clustering methods are an important tool to enumerate and describe the different coherent kinds of Gamma Ray Bursts (GRBs). But their performance can be affected by a number of factors such as the choice of clustering algorithm and inherent associated assumptions, the inclusion of variables in clustering, nature of initialization methods used or the iterative algorithm or the criterion used to judge the optimal number of groups supported by the data. We analyzed GRBs from the BATSE 4Br catalog using k-means and Gaussian Mixture Models-based clustering methods and found that after accounting for all the above factors, all six variables -different subsets of which have been used in the literature -and that are, namely, the flux duration variables (T 50 , T 90 ), the peak flux (P 256 ) measured in 256-millisecond bins, the total fluence (F t ) and the spectral hardness ratios (H 32 and H 321 ) contain information on clustering. Further, our analysis found evidence of five different kinds of GRBs and that these groups have different kinds of dispersions in terms of shape, size and orientation. In terms of duration, fluence and spectrum, the five types of GRBs were characterized as intermediate/faint/intermediate, long/intermediate/soft, intermediate/intermediate/intermediate, short/faint/hard and long/bright/intermediate.

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“…Maximum Likelihood Estimation is an essential algorithm in parameter estimation. Among these algorithms, the expectation-maximization algorithm is the most commonly used [48] [49]. The Cluster Analysis Statistical Test algorithm is also considered a clustering algorithm based on a probability model [50].…”

Section: A Partition Clustering Methodsmentioning

confidence: 99%

Teaching Teacher Recommendation Method Based on Fuzzy Clustering and Latent Factor Model

Yao

Deng

2020

IEEE Access

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The EM Algorithm and Extensions.

Cited by 25 publications

References 0 publications

Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Gaussian-mixture-model-based cluster analysis finds five kinds of gamma-ray bursts in the BATSE catalogue

Teaching Teacher Recommendation Method Based on Fuzzy Clustering and Latent Factor Model

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