Support Vector Machine Training for Improved Hidden Markov Modeling

We present a discriminative training algorithm, that uses support vector machines (SVMs), to improve the classification of discrete and continuous output probability hidden Markov models (HMMs). The algorithm uses a set of maximum-likelihood (ML) trained HMM models as a baseline system, and an SVM training scheme to rescore the results of the baseline HMMs. It turns out that the rescoring model can be represented as an unnormalized HMM. We describe two algorithms for training the unnormalized HMM models for both the discrete and continuous cases. One of the algorithms results in a single set of unnormalized HMMs that can be used in the standard recognition procedure (the Viterbi recognizer), as if they were plain HMMs. We use a toy problem and an isolated noisy digit recognition task to compare our new method to standard ML training. Our experiments show that SVM rescoring of hidden Markov models typically reduces the error rate significantly compared to standard ML training.     

Application of the Gibbs distribution to hidden Markov modeling inspeaker independent isolated word recognition

A method of integrating the Gibbs distributions (GDs) into hidden Markov models (HMMs) is presented. The probabilities of the hidden state sequences of HMMs are modeled by GDs in place of the transition probabilities. The GDs offer a general way in modeling neighbor interactions of Markov random fields where the Markov chains in HMMs are special cases. An algorithm for estimating the model parameters is developed based on Baum reestimation, and an algorithm for computing the probability terms is developed using a lattice structure. The GD models were used for experiments in speech recognition on the TI speaker-independent, isolated digit database. The observation sequences of the speech signals were modeled by mixture Gaussian autoregressive densities. The energy functions of the GDs were developed using very few parameters and proved adequate in hidden layer modeling. The results of the experiments showed that the GD models performed at least as well as the HMM models     

Image segmentation using hidden Markov Gauss mixture models.

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.     

Music Analysis Using Hidden Markov Mixture Models

We develop a hidden Markov mixture model based on a Dirichlet process (DP) prior, for representation of the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, and this naturally reveals the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved in two ways: 1) via a rigorous Markov chain Monte Carlo method; and 2) approximately and efficiently via a variational Bayes formulation. Using DP HMM mixture models in a Bayesian setting, we propose a novel scheme for music analysis, highlighting the effectiveness of the DP HMM mixture model. Music is treated as a time-series data sequence and each music piece is represented as a mixture of HMMs. We approximate the similarity of two music pieces by computing the distance between the associated HMM mixtures. Experimental results are presented for synthesized sequential data and from classical music clips. Music similarities computed using DP HMM mixture modeling are compared to those computed from Gaussian mixture modeling, for which the mixture modeling is also performed using DP. The results show that the performance of DP HMM mixture modeling exceeds that of the DP Gaussian mixture modeling.     

Upper Bound Kullback–Leibler Divergence for Transient Hidden Markov Models

This paper reports an upper bound for the Kullback–Leibler divergence (KLD) for a general family of transient hidden Markov models (HMMs). An upper bound KLD (UBKLD) expression for Gaussian mixtures models (GMMs) is presented which is generalized for the case of HMMs. Moreover, this formulation is extended to the case of HMMs with nonemitting states, where under some general assumptions, the UBKLD is proved to be well defined for a general family of transient models. In particular, the UBKLD has a computationally efficient closed-form for HMMs with left-to-right topology and a final nonemitting state, that we refer to as left-to-right transient HMMs. Finally, the usefulness of the closed-form expression is experimentally evaluated for automatic speech recognition (ASR) applications, where left-to-right transient HMMs are used to model basic acoustic-phonetic units. Results show that the UBKLD is an accurate discrimination indicator for comparing acoustic HMMs used for ASR.      

Automatic identification of audio recordings based on statistical modeling

This paper describes a methodology for the automatic identification of audio recordings of ethnic music. The identification is based on an application of hidden Markov models (HMMs), which are automatically built from a representation of the music pieces to be identified. States of the HMMs are labeled with music events, and the transition and observation probabilities are directly computed from the information on the music piece. The recordings are modeled by a set of acoustic features that are computed according with the characteristics of the music events. Three alternative approaches, based on typical applications of HMMs, are proposed to perform the identification. Tests carried out on collections of recordings showed that the methodology can achieve good results, and the identification rate is high enough to suggest applications for automatic retrieval of metadata and for the identification of alternative recordings of the same piece.     

Complexity reduction in fixed-lag smoothing for hidden Markovmodels

We investigate approximate smoothing schemes for a class of hidden Markov models (HMMs), namely, HMMs with underlying Markov chains that are nearly completely decomposable. The objective is to obtain substantial computational savings. Our algorithm can not only be used to obtain aggregate smoothed estimates but can be used also to obtain systematically approximate full-order smoothed estimates with computational savings and rigorous performance guarantees, unlike many of the aggregation methods proposed earlier     

Activity modeling using event probability sequences.

Changes in motion properties of trajectories provide useful cues for modeling and recognizing human activities. We associate an event with significant changes that are localized in time and space, and represent activities as a sequence of such events. The localized nature of events allows for detection of subtle changes or anomalies in activities. In this paper, we present a probabilistic approach for representing events using the hidden Markov model (HMM) framework. Using trained HMMs for activities, an event probability sequence is computed for every motion trajectory in the training set. It reflects the probability of an event occurring at every time instant. Though the parameters of the trained HMMs depend on viewing direction, the event probability sequences are robust to changes in viewing direction. We describe sufficient conditions for the existence of view invariance. The usefulness of the proposed event representation is illustrated using activity recognition and anomaly detection. Experiments using the indoor University of Central Florida human action dataset, the Carnegie Mellon University Credo Intelligence, Inc., Motion Capture dataset, and the outdoor Transportation Security Administration airport tarmac surveillance dataset show encouraging results.     

On-line identification of hidden Markov models via recursiveprediction error techniques

An on-line state and parameter identification scheme for hidden Markov models (HMMs) with states in a finite-discrete set is developed using recursive prediction error (RPE) techniques. The parameters of interest are the transition probabilities and discrete state values of a Markov chain. The noise density associated with the observations can also be estimated. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to show that the algorithms converge for a wide variety of initializations. In addition, an improved version of an earlier proposed scheme (the Recursive Kullback-Leibler (RKL) algorithm) is presented with a parameterization that ensures positivity of transition probability estimates     

Asymptotic smoothing errors for hidden Markov models

In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant /spl epsiv/, which is a measure of the frequency of change. Thus, when /spl epsiv//spl rarr/0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(/spl epsiv/). These theoretical predictions are confirmed by a series of simulations.     

2维隐马尔可夫模型的基本问题求解

研究了2维隐马尔可夫模型的三个基本问题,包括概率评估问题、最优状态问题和参数估计问题.通过把2维隐马尔可夫模型行或者列上的状态序列看作一个马尔可夫模型,从理论上分别给出了解决这三个基本问题的新算法;计算机仿真对新算法的实现和运行作了进一步的说明.     

A minimum discrimination information approach for hidden Markovmodeling

An iterative approach for minimum-discrimination-information (MDI) hidden Markov modeling of information sources is proposed. The approach is developed for sources characterized by a given set of partial covariance matrices and for hidden Markov models (HMMs) with Gaussian autoregressive output probability distributions (PDs). The approach aims at estimating the HMM which yields the MDI with respect to all sources that could have produced the given set of partial covariance matrices. Each iteration of the MDI algorithm generates a new HMM as follows. First, a PD for the source is estimated by minimizing the discrimination information measure with respect to the old model over all PDs which satisfy the given set of partial covariance matrices. Then a new model that decreases the discrimination information measure between the estimated PD of the source and the PD of the old model is developed. The problem of estimating the PD of the source is formulated as a standard constrained minimization problem in the Euclidean space. The estimation of a new model given the PD of the source is done by a procedure that generalizes the Baum algorithm. The MDI approach is shown to be a descent algorithm for the discrimination information measure, and its local convergence is proved     

Hidden Markov modeling of flat fading channels

Hidden Markov models (HMMs) are a powerful tool for modeling stochastic random processes. They are general enough to model with high accuracy a large variety of processes and are relatively simple allowing us to compute analytically many important parameters of the process which are very difficult to calculate for other models (such as complex Gaussian processes). Another advantage of using HMMs is the existence of powerful algorithms for fitting them to experimental data and approximating other processes. In this paper, we demonstrate that communication channel fading can be accurately modeled by HMMs, and we find closed-form solutions for the probability distribution of fade duration and the number of level crossings     

MAP decoding in channels with memory

The expectation-maximization (EM) algorithm is popular in estimating the parameters of various statistical models. We consider applications of the EM algorithm to the maximum a posteriori (MAP) sequence decoding assuming that sources and channels are described by hidden Markov models (HMMs). The HMMs can accurately approximate a large variety of communication channels with memory and, in particular, wireless fading channels with noise. The direct maximization of the a posteriori probability (APP) is too complex. The EM algorithm allows us to obtain the MAP sequence estimation iteratively. Since each step of the EM algorithm increases the APP, the algorithm can improve the performance of any decoding procedure     

SAR图像小波域隐Markov模型中状态参数的Turbo迭代估计

利用小波域隐Markov模型能够有效地改善合成孔径雷达(SAR)图像信息提取的效果,而乘性斑点噪声影响下的隐状态的估计是其中的关键问题,目前该问题还没有得到有效地解决.借用信息论领域中的Turbo迭代译码原理,针对SAR图像信号,提出一种新的隐状态的Turbo迭代估计方法.该方法在两个不相关的子空间上分别采用不同的约束条件对隐状态进行轮流地估计,并将其后验概率作为一种外信息进行交换.实验结果证明该方法具有优良的估计结果,并且收敛速度较快.     

Optimization of trajectory signal processing in a radar system with digital synthesis of antenna aperture using hidden Markov models

Function of radar relief in the space of states is determined using hidden Markov models. An optimal algorithm for processing of trajectory signal of radar system with digital synthesis of antenna aperture is developed with allowance for equivalent discrete representation of the continuous function of radar relief. The application of the Gaussian approximation of the conditional a posteriori probability density of the radar-relief function yields an acceptable quasi-optimal filtering algorithm. The efficiency of the synthesized recurrence algorithm is proven with the aid of statistical simulation.     

A fused hidden Markov model with application to bimodal speech processing

This paper presents a novel fused hidden Markov model (fused HMM) for integrating tightly coupled time series, such as audio and visual features of speech. In this model, the time series are first modeled by two conventional HMMs separately. The resulting HMMs are then fused together using a probabilistic fusion model, which is optimal according to the maximum entropy principle and a maximum mutual information criterion. Simulations and bimodal speaker verification experiments show that the proposed model can significantly reduce the recognition errors in noiseless or noisy environments.     

Analyticity of Entropy Rate of Hidden Markov Chains

We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters     

基于不同隐马尔科夫模型的图像识别方法

为了更详细地研究隐马尔科夫模型在图像识别中的应用,以指纹识别为例,纵向总结了几种基于隐马尔科夫模型的指纹图像识别算法,包括一维隐马尔科夫模型、伪二维隐马尔科夫模型、二维模型及一维模型组。分别从时间复杂度、识别精确度等方面总结出这四种隐马尔科夫模型在图像识别时的优缺点,得出不同待识别图像适合使用的识别模型的结论。