Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameter estimation in hidden fuzzy Markov random fields and image segmentation
Graphical Models and Image Processing
Automatic Segmentation of Acoustic Musical Signals Using Hidden Markov Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Off-Line Handwritten Word Recognition Using a Hidden Markov Model Type Stochastic Network
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inference in Hidden Markov Models (Springer Series in Statistics)
Inference in Hidden Markov Models (Springer Series in Statistics)
Unsupervised image segmentation using triplet Markov fields
Computer Vision and Image Understanding
Unsupervised signal restoration using hidden Markov chains with copulas
Signal Processing
Multisensor triplet Markov chains and theory of evidence
International Journal of Approximate Reasoning
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Unsupervised restoration of hidden nonstationary Markov chains using evidential priors
IEEE Transactions on Signal Processing - Part II
Kalman Filtering in Triplet Markov Chains
IEEE Transactions on Signal Processing
An equivalence of the EM and ICE algorithm for exponential family
IEEE Transactions on Signal Processing
Signal and image segmentation using pairwise Markov chains
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Unsupervised data classification using pairwise Markov chains with automatic copulas selection
Computational Statistics & Data Analysis
Efficient Bayesian estimation of the multivariate Double Chain Markov Model
Statistics and Computing
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The hidden Markov chain (HMC) model is a couple of random sequences (X,Y), in which X is an unobservable Markov chain, and Y is its observable noisy version. Classically, the distribution p(y|x) is simple enough to ensure the Markovianity of p(x|y), that enables one to use different Bayesian restoration techniques. HMC model has recently been extended to ''pairwise Markov chain'' (PMC) model, in which one directly assumes the Markovianity of the pair Z=(X,Y), and which still enables one to recover X from Y. Finally, PMC has been extended to ''triplet Markov chain'' (TMC) model, which is obtained by adding a third chain U and considering the Markovianity of the triplet T=(X,U,Y). When U is not too complex, X can still be recovered from Y. Then U can model different situations, like non-stationarity or semi-Markovianity of (X,Y). Otherwise, PMC and TMC have been extended to pairwise ''partially'' Markov chains (PPMC) and triplet ''partially'' Markov chains (TPMC), respectively. In a PPMC Z=(X,Y) the distribution p(x|y) is a Markov distribution, but p(y|x) may not be and, similarly, in a TPMC T=(X, U, Y) the distribution p(x,u|y) is a Markov distribution, but p(y|x,u) may not be. However, both PPMC and TPMC can enable one to recover X from Y, and TPMC include different long-memory noises. The aim of this paper is to show how a particular Gaussian TPMC can be used to segment a discrete signal hidden with long-memory noise. An original parameter estimation method, based on ''Iterative Conditional Estimation'' (ICE) principle, is proposed and some experiments concerned with unsupervised segmentation are provided. The particular unsupervised segmentation method used in experiments can also be seen as identification of different stationarities in fractional Brownian noise, which is widely used in different problems in telecommunications, economics, finance, or hydrology.