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Finite mixture of hidden Markov models for tensor-variate time series data

ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2024年第3期18卷 545-562页

作者： Asilkalkan, Abdullah Zhu, Xuwen Sarkar, Shuchismita Univ Alabama Dept Informat Syst Stat & Management Sci Tuscaloosa AL 35487 USA Bowling Green State Univ Dept Appl Stat & Operat Res Bowling Green OH 43403 USA

The need to model data with higher dimensions, such as a tensor-variate framework where each observation is considered a three-dimensional object, increases due to rapid improvements in computational power and data storage capabilities. In this study, a finite mixture of hidden Markov model for tensor-variate time series data is developed. Simulation studies demonstrate high classification accuracy for both cluster and regime IDs. To further validate the usefulness of the proposed model, it is applied to real-life data with promising results.

关键词： Finite mixture model Hidden Markov model forward-backward algorithm Tensor-variate time series

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Measuring the Influence of Observations in HMMs Through the Kullback-Leibler Distance

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IEEE SIGNAL PROCESSING LETTERS 2013年第2期20卷 145-148页

作者： Perduca, Vittorio Nuel, Gregory Univ Paris 05 Lab MAP5 Sorbonne Paris Cite France CNRS Sorbonne Paris Cite France

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting meaningful observations} in HMM data series.

关键词： forward-backward algorithm Hidden Markov Models local outlier factor outlier detection relative entropy

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Path partitions and forward-only trellis algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第1期49卷 38-52页

作者： Ma, X Kavcic, A Harvard Univ Div Engn & Appl Sci Cambridge MA 02138 USA

This is a semitutorial paper on trellis-based algorithms. We argue that most decoding/detection algorithms described on trellises can be formulated as path-partitioning algorithms, with proper definitions of mappings from subsets of paths to metrics of subsets. Thereby, the only two operations needed are path-concatenation and path-collection, which play the roles of multiplication and addition, respectively. Furthermore, we show that the trellis structure permits the path-partitioning algorithms to be formulated as forward-only algorithms (with structures resembling the Viterbi algorithm), thus eliminating the need for backward computations regardless of what task needs to be performed on the trellis. While all of the actual decoding/detection algorithms presented here are rederivations of variations of previously known methods, we believe that the exposition of the algorithms in a unified manner as forward-only path-partitioning algorithms is the most intuitive manner in which to generalize the Viterbi algorithm. We also believe that this approach may, in fact, influence the practical implementation of the algorithms as well as influence the construction of other forward-only algorithms (e.g., byte-wise forward-only detection algorithms).

关键词： Babl-Cocke-Jelinek-Raviv (BCJR) algorithm forward-backward algorithm forward-only algorithm Markov processes sum-product algorithm trellis graph Viterbi algorithm

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A Proximal Interior Point algorithm with Applications to Image Processing

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2020年第6-7期62卷 919-940页

作者： Chouzenoux, Emilie Corbineau, Marie-Caroline Pesquet, Jean-Christophe Univ Paris Saclay Inria Saclay Cent Supelec CVN 9 Rue Joliot Curie F-91190 Gif Sur Yvette France

In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself is analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

关键词： Interior point methods Proximity operator Constrained optimization forward-backward algorithm Variable metric Line search Armijo strategy Hyperspectral unmixing Geometry-texture decomposition

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Turbo Segmentation of Textured Images

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2011年第1期33卷 16-29页

作者： Lehmann, Frederic TELECOM SudParis Inst TELECOM Dept CITI F-91011 Evry France

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.

关键词： Texture segmentation Markov random field hidden Markov autoregressive model factor graph forward-backward algorithm turbo processing

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Hidden hybrid Markov/semi-Markov chains

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2005年第3期49卷 663-688页

作者： Guédon, Y Univ Montpellier 2 INRA CNRS UMRCIRAD F-34398 Montpellier France

Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains for the modeling of short or medium size homogeneous zones along sequences but also enables the modeling of long zones with Markovian states. The forward-backward algorithm, which in particular enables to implement efficiently the E-step of the EM algorithm, and the Viterbi algorithm for the restoration of the most likely state sequence are derived. It is also shown that macro-states, i.e. series-parallel networks of states with common observation distribution, are not a valid alternative to semi-Markovian states but may be useful at a more macroscopic level to combine Markovian states with semi-Markovian states. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants. (c) 2004 Elsevier B.V. All rights reserved.

关键词： forward-backward algorithm hidden Markov chain hidden semi-Markov chain macro-state plant structure analysis smoothing algorithm viterbi algorithm

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A PARALLEL SPLITTING METHOD FOR COUPLED MONOTONE INCLUSIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2010年第5期48卷 3246-3270页

作者： Attouch, Hedy Briceno-Arias, Luis M. Combettes, Patrick L. Univ Paris 06 UPMC Lab Jacques Louis Lions UMR CNRS 7598 F-75005 Paris France Equipe Combinatoire & Optimisat UMR CNRS 7090 F-75005 Paris France Univ Montpellier 2 Inst Math & Modelisat Montpellier UMR CNRS 5149 F-34095 Montpellier 5 France

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.

关键词： coupled systems demiregular operator evolution inclusion forward-backward algorithm maximal monotone operator operator splitting parallel algorithm weak convergence

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Correcting Insertions/Deletions in DPPM Using Hidden Markov Model

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IEEE ACCESS 2020年 8卷 46417-46426页

作者： Chen, Weigang Wang, Lixia Han, Changcai Tianjin Univ Sch Microelect Tianjin 300072 Peoples R China

Differential pulse-position modulation (DPPM) shows significant power and bandwidth efficiency, but suffers from serious insertion/deletion and substitution errors if the DPPM soft-decision symbol-by-symbol detection method is used. In this paper, based on the DPPM transmission scheme combining the watermark with the low-density parity-check (LDPC) code, and the equivalent source and channel models, we propose an efficient decoding scheme using hidden Markov model (HMM). Specifically, with the known watermark and the equivalent source and channel models, a hidden markov model is first established to estimate the insertion/deletion errors of the received symbols. Then, a hard-decision forward-backward algorithm is used to recover synchronization and output the estimate of the codeword. Finally, Belief-Propagation (BP) decoding algorithm in the logarithmic domain is performed to correct the residual substitution errors. Simulation results reveal that compared with the decoding scheme using the dynamic programming (DP) and Viterbi algorithms, the proposed decoding scheme has superior performance in correcting insertion, deletion and substitution errors in DPPM transmission.

关键词： DPPM insertion/deletion hidden Markov model (HMM) forward-backward algorithm

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Virtual Full-Duplex Distributed Spatial Modulation: A New Protocol for Cooperative Diversity

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IEEE ACCESS 2019年 7卷 87634-87646页

作者： Shehni, Amir Flanagan, Mark F. Univ Coll Dublin Sch Elect & Elect Engn Dublin D04 V1W8 Ireland

Spatial modulation, a multi-antenna technology which uses the antenna index as an additional means of conveying information, is an emerging technology for modem wireless communications. In this paper, a new distributed version of spatial modulation is proposed which achieves virtual full-duplex communication (VFD-DSM) in order to increase system throughput. This throughput improvement is achieved by allowing the source to transmit new data while the relays implicitly forward the source's data in every time slot (via the index of the active relay) while explicitly transmitting their own data (via a conventional modulation technique). Motivated by the achievable throughput improvement with VFD-DSM, two maximum a posteriori (MAP) detection methods are proposed for implementation at the destination node: the first, called local MAP, is based on processing the signals received over two or three consecutive time slots, while the second, called global MAP, is based on symbol-error-rate optimal detection over an entire frame of data. For each MAP detection method, an error-aware version of the detector is also proposed which takes into account the demodulation error rate at the relays;this can achieve an extra BER advantage at the cost of additional complexity and an increased channel state information (CSI) requirement. Simulation results demonstrate that the proposed VFD-DSM protocol can provide an improved BER compared to the baseline protocol of successive relaying, while also providing a significant increase in the overall throughput since the relays can forward the source symbols while simultaneously transmitting their own data. The proposed VFD-DSM detectors are shown to provide a range of design choices offering different tradeoffs between BER performance and computational complexity. Finally, the impact of the data frame length in VFD-DSM on the error rate performance and system throughput is investigated, and it is shown how to choose the optimal frame length for

关键词： Spatial modulation full-duplex communication relay networks forward-backward algorithm

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Inpainting by Flexible Haar-Wavelet Shrinkage

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SIAM JOURNAL ON IMAGING SCIENCES 2008年第3期1卷 273-293页

作者： Chan, R. H. Setzer, S. Steidl, G. Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China Univ Mannheim Dept Math & Comp Sci D-68131 Mannheim Germany

We present novel wavelet-based inpainting algorithms. Applying ideas from anisotropic regularization and diffusion, our models can better handle degraded pixels at edges. We interpret our algorithms within the framework of forward-backward splitting methods in convex analysis and prove that the conditions for ensuring their convergence are fulfilled. Numerical examples illustrate the good performance of our algorithms.

关键词： image inpainting anisotropic methods forward-backward algorithm wavelet shrinkage

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