Contextual Estimation Of Hidden Markov Chains With Application To Image Segmentation

Derrode, Stéphane; Benyoussef, Lamia; Pieczynski, Wojciech

doi:10.1109/icassp.2006.1660436

Cited by 5 publications

(4 citation statements)

References 5 publications

(5 reference statements)

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“…a) Hidden Markov Models (HMMs): Hidden Markov Models (HMMs) are a class of latent data models appropriate for sequential data. They are widely used in many application domains, including speech recognition, image analysis, time series prediction [14], [15], etc. In an HMM, the observation sequence (or a time series) y i = (y i1 , .…”

Section: B Related Work On Model-based Clustering For Time Series 1)mentioning

confidence: 99%

Model-based clustering with Hidden Markov Model regression for time series with regime changes

Chamroukhi

Samé²,

Aknin³

et al. 2011

The 2011 International Joint Conference on Neural Networks

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This paper introduces a novel model-based clustering approach for clustering time series which present changes in regime. It consists of a mixture of polynomial regressions governed by hidden Markov chains. The underlying hidden process for each cluster activates successively several polynomial regimes during time. The parameter estimation is performed by the maximum likelihood method through a dedicated Expectation-Maximization (EM) algorithm. The proposed approach is evaluated using simulated time series and real-world time series issued from a railway diagnosis application. Comparisons with existing approaches for time series clustering, including the stand EM for Gaussian mixtures, K-means clustering, the standard mixture of regression models and mixture of Hidden Markov Models, demonstrate the effectiveness of the proposed approach.

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Section: B Related Work On Model-based Clustering For Time Series 1)mentioning

confidence: 99%

Model-based clustering with Hidden Markov Model regression for time series with regime changes

Chamroukhi

Samé²,

Aknin³

et al. 2011

The 2011 International Joint Conference on Neural Networks

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“…Hidden Markov models (HMMs) have been used to model various types of data: discrete, continuous, univariate, multivariate, mixed and mixture data (Zucchini & MacDonald 2009). Consequently, they have been widely applied in many fields, such as econometrics (Hamilton 1989;Billio, Monfort & Robert 1999); finance (Bhar & Hamori 2006); speech recognition (Rabiner 1989;Derrode, Benyoussef & Pieczynski 2006); and psychology (Visser, Raijmakers & Molenaar 2002).…”

Section: Introductionmentioning

confidence: 99%

Using hidden Markov models to model spatial dependence in a network

Kadhem

Hewson

Kaimi

2018

Aus NZ J of Statistics

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Summary This study considers spatial dependence in the number of injury crashes reported on a road network. The aggregated crash counts are considered realisations of a Poisson random variable; thus, we model both over‐dispersion and serial correlation using the Poisson hidden Markov model (PHMM). PHMMs have typically been used for modelling temporal dependence, but they have rarely been used to model spatial dependence. Our interest, however, is specifically in relation to an underlying point process which is constrained to occur on a network. We illustrate the use of the PHMM with police‐reported data on injury road collisions on selected motorways in the United Kingdom over a 5‐year period (2010–2014). We use officially recorded estimates of traffic volume as an exposure variable. The aim is to identify highway segments which might have distinctly high crash rates. To do this, we first select an optimal model in terms of the number of latent states. As we use a Bayesian approach, we can assign a posterior classification probability to each segment in terms of membership of the various underlying risk states. Model fitting is conducted using the Markov chain Monte Carlo approach; we develop a new modified version of the Akaike Information Criterion and Bayesian Information Criterion, approximated from a Bayesian framework, to select the best model in terms of number of states.

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“…Consequently, they have been widely applied in many fields, such as econometrics (Hamilton, 1989;Billio et al, 1999); finance (Bhar and Hamori, 2004); speech recognition (Rabiner, 1989;Derrode, 2006); and psychology (Visser et al, 2002). One important issue that is often discussed after fitting models is the model choice issue.…”

Section: Introductionmentioning

confidence: 99%

Recursive Deviance Information Criterion for the Hidden Markov Model

Kadhem¹,

Hewson²,

Kaimi³

2015

IJSP

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In Bayesian model selection, the deviance information criterion (DIC) has become a widely used criterion. It is however not defined for the hidden Markov models (HMMs). In particular, the main challenge of applying the DIC for HMMs is that the observed likelihood function of such models is not available in closed form. A closed form for the observed likelihood function can be obtained either by summing all possible hidden states of the complete likelihood using the so-called the forward recursion, or via integrating out the hidden states in the conditional likelihood. Hence, we propose two versions of the DIC to the model choice problem in HMMs context, namely, the recursive deviance-based DIC and the conditional likelihood-based DIC. In this paper, we compare several normal HMMs after they are estimated by Bayesian MCMC method. We conduct a simulation study based on synthetic data generated under two assumptions, namely diversity in the heterogeneity level and also the number of states. We show that the recursive deviance-based DIC performs well in selecting the correct model compared with the conditional likelihood-based DIC that prefers the more complicated models. A real application involving the waiting time of Old Faithful Geyser data was also used to check those criteria. All the simulations were conducted in Python v.2.7.10, available from first author on request.

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Contextual Estimation Of Hidden Markov Chains With Application To Image Segmentation

Cited by 5 publications

References 5 publications

Model-based clustering with Hidden Markov Model regression for time series with regime changes

Model-based clustering with Hidden Markov Model regression for time series with regime changes

Using hidden Markov models to model spatial dependence in a network

Recursive Deviance Information Criterion for the Hidden Markov Model

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