Unsupervised Segmentation of Random Discrete Data Hidden With Switching Noise Distributions

Boudaren, Mohamed El Yazid; Monfrini, Emmanuel; Pieczynski, Wojciech

doi:10.1109/lsp.2012.2209639

Cited by 24 publications

(11 citation statements)

References 11 publications

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“…A hidden Markov model can be considered a generalization of a mixture model where the hidden variables (or latent variables), which control the mixture component to be selected for each observation, are related through a Markov process rather than independent of each other. Recently, hidden Markov models have been generalized to pairwise Markov models and triplet Markov models which allow consideration of more complex data structures [21] [22] and the modeling of non stationary data [23] [24].…”

Section: A Definition Of Hidden Markov Modelmentioning

confidence: 99%

Distributed fault detection based on HMM for Wireless Sensor Networks

Saihi

Boussaid

Zouinkhi

et al. 2015

2015 4th International Conference on Systems and Control (ICSC)

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In their practical applications, Wireless Sensor Networks (WSNs) can experience faults during running. Furthermore, faulty data collected in the base station might lead to a wrong judgement.Since the whole system's performance require the accuracy of data, node fault detection is necessary. Motivated by the requirement of fault detection performance, we propose a distributed fault detection algorithm for wireless senor networks based on Hidden Markov Model (HMM). Firstly, a density of probability method is presented to obtain the possibility of translation of state for each node in the network. Then, a HMM is introduced to characterize the tendency of each node to be faulty. Finally, a distributed fault detection algorithm is proposed based on the HMM. Simulation results show that the proposed HMM-based fault detection achieves high detection accuracy. Index Terms-Hidden Markov Model, density of probability, Wireless Sensor Networks, Distributed Fault Detection 978-1-4799-8318-6/15/$31.00 ©2015 IEEE

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Section: A Definition Of Hidden Markov Modelmentioning

confidence: 99%

Distributed fault detection based on HMM for Wireless Sensor Networks

Saihi

Boussaid

Zouinkhi

et al. 2015

2015 4th International Conference on Systems and Control (ICSC)

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“…One could further generalize the process, and introduce dependence of on previous samples of as well as on . The reader is referred to the work in [6], [10], [23]- [25], [33], [34] for possible extensions along these lines. A possible benefit of the latter model is that it can better capture the correlation of the process .…”

Section: Commentsmentioning

confidence: 99%

Causal Recursive Parameter Estimation for Discrete-Time Hidden Bivariate Markov Chains

Ephraim

Mark

2015

IEEE Trans. Signal Process.

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An algorithm for causal recursive parameter estimation of a discrete-time hidden bivariate Markov chain is developed. In this model, a discrete-time bivariate Markov chain is observed through a discrete-time memoryless channel. The algorithm relies on the EM-based recursive approach developed by Stiller and Radons for hidden Markov models. A distinct advantage of the discrete-time hidden bivariate Markov chain model is that the sojourn time distribution of its observable process in each state is phase-type rather than geometric as in the hidden Markov model. Phase-type distributions can approximate any desired sojourn time distribution. Particular phase-type distributions include mixtures and convolutions of geometric distributions. The parameter estimation algorithm requires causal recursive estimation of the relevant statistics in each EM step. These statistics include the number of jumps of the bivariate Markov chain from one state to another, including self transitions, in the given observation interval, and first-and second-order statistical averages of the observable process in each state when the memoryless channel is Gaussian. We develop the explicit recursions and demonstrate the performance of the algorithm in estimating the model's parameter and its sojourn time distribution in a numerical example.

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“…is not necessarily Markovian. This context has already proven very effective in image segmentation for modeling multiple-stationaries (Lanchantin et al, 2011;Boudaren et al, 2012a), in hidden semi-Markov chains (Lapuyade-Lahorgue et Pieczynski, 2011a) or in hidden evidential Markov chains (Pieczynski, 2007 ;Boudaren et al, 2012b ;Ramasso et Denoeux, 2013), but is novel in optimal statistical filtering. Simulations are provided to illustrate the value of the new modeling in the context of non-stationary on-line filtering of time-series.…”

Section: Extended Abstractmentioning

confidence: 99%

“…n'est pas nécessairement markovien, s'avèrent très efficaces en situations non stationnaires (Lanchantin et al, 2011 ;Boudaren et al, 2012a), ce qui est à l'origine de la présente étude. En effet, ainsi que nous allons le montrer, il est possible d'étendre la famille MCCLSM des triplets ) , , (…”

Section: Introductionunclassified

Filtrage statistique optimal rapide dans des systèmes linéaires à sauts non stationnaires

Abbassi

Derrode²,

Desbouvries

et al. 2014

Traitement du signal

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International audienceRESUME. Nous traitons du problème de filtrage statistique optimal dans des systèmes à sauts. Nous considérons trois processus : un processus continu caché X, un processus continu observé Y, et un processus discret caché R modélisant les « sauts », qui peuvent être vus comme les changements aléatoires des paramètres régissant localement les distributions markoviennes du couple (X,Y). Nous nous intéressons à une famille récente de modèles dans laquelle il est possible de mettre en place un filtrage optimal rapide, dont la complexité est linéaire en temps. Nous étendons cette famille en introduisant un quatrième processus discret fini U permettant de modéliser les possibles non-stationnarités du triplet (X, R, Y). Nous montrons que les filtrages optimaux rapides demeurent possibles dans la famille étendue et nous illustrons leur intérêt via quelques simulations. ABSTRACT. This paper deals with optimal statistical filtering in jump systems. We consider three random sequences: a hidden real-valued process X, an observed real-valued process Y and a hidden discrete process R modeling jumps that can be interpreted as random switches in the parameters governing locally the Markovian distributions of the pairwise process (X,Y). We focus on a recent family of models in which it is possible to implement a fast optimal filtering, whose complexity is linear in time. We extend this family by introducing a fourth hidden discrete process U to model possible non-stationarity in triplet (X, R, Y). We show that fast optimal filtering remains possible in the extended family and illustrate their interest via some simulations. MOTS-CLES : Système linéaire gaussien à sauts. Filtrage optimal exact. Modèle caché conditionnellement linéaire à sauts markoviens. Modèle caché conditionnellement linéaire à sauts marginalement markoviens

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Unsupervised Segmentation of Random Discrete Data Hidden With Switching Noise Distributions

Cited by 24 publications

References 11 publications

Distributed fault detection based on HMM for Wireless Sensor Networks

Distributed fault detection based on HMM for Wireless Sensor Networks

Causal Recursive Parameter Estimation for Discrete-Time Hidden Bivariate Markov Chains

Filtrage statistique optimal rapide dans des systèmes linéaires à sauts non stationnaires

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