Real‐Time Gesture–Based Communication Using Possibility Theory–Based Hidden Markov Model

Exploring correct patterns from low‐frequency time‐series data is challenging. For resolving this problem, the concept of possibility theory–based hidden Markov model (PTBHMM) has been proposed. In this article, all three fundamental problems (evaluation, decoding, and learning) of conventional HMM have been addressed using possibility theory. For handling uncertainty, we have used an axiomatic approach of possibility theory proposed by Zadeh. The time complexity of existing solutions of HMM (forward, backward, Viterbi, and Baum Welch) and proposed possibility‐based solutions has been calculated and compared. From the comparison result, it has been found that PTBHMM has lesser time complexity and hence will be more suitable for real‐time gesture–based communication.     

一种基于HMM的动态语音模式时间归一化方法

研究了利用隐马尔可夫模型(HMM)对动态语音模式进行时间归一化的方法。引入了借助于HMM对语音基元观测序列所做的一种分段，这种分段被称之为语音基元观测序列的HMM全状态分段，并且定义了HMM全状态分段的符合度。根据HMM全状态分段的符合度确定了语音基元观测序列的最优HMM全状态分段，通过最优HMM全状态分段把语音基元观测序列转换为固定维数的向量，从而实现了动态语音模式的时间归一化。将动态语音模式的这一时间归一化方法在结合HMM和人工神经网络(ANN)的混合语音识别方法中进行了应用，实验结果表明这一时间归一化方法的有效性。     

Lumpable hidden Markov models-model reduction and reducedcomplexity filtering

This paper is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms     

基于进化HMM模型的动态Agent系统建模方法

提出一种基于隐式Markov模型（HMM）的进化建模方法．使用进化算法随机搜索HMM的模型空间,自动选择HMM的结构和参数-完成对动态智能体系统行为的建模,学习智能体对周围环境的分割和反映方式．实验结果表明,该方法可以很好地搜索HMM的模型空间,并且避免了人工确定HMM模型结构的困难和手工设计模型所需的多次反复．     

An M-ary detection approach for asset allocation

We develop a continuous-time asset allocation model which incorporates both model uncertainty and structural changes in economic conditions. A “dynamic” M-ary detection framework for a continuous-time hidden Markov chain partially observed in a Gaussian process is used to model the price dynamics of the risky asset and the hidden states of an economy. The goal of an investor is to select an optimal asset portfolio mix so as to maximize the expected utility of terminal wealth. Filtering theory is used first to turn the problem into one with complete observations and then to derive M-ary detection filters for the hidden system. The Hamilton-Jacobi-Bellman dynamic programming approach is used to solve the asset allocation problem with complete observations. An explicit solution is obtained for the power utility case.     

基于改进粒子群算法的隐马尔可夫模型训练

针对隐马尔可夫模型传统训练算法易收敛于局部极值的问题,提出一种带极值扰动的自适应调整惯性权重和加速系数的粒子群算法,将改进后的粒子群优化算法引入到隐马尔可夫模型的训练中,分别对隐马尔可夫模型的状态数与参数进优化.通过对手写数字识别的实验说明,提出的基于改进粒子群优化算法的隐马尔可夫模型训练算法与传统隐马尔可夫模型训练算法Baum-Welch算法相比,能有效地跳出局部极值,从而使训练后的隐马尔可夫模型具有较高的识别能力.     

基于手势识别的机器人人机交互技术研究

研究了基于视觉的动态手势识别技术,采用基于肤色的高斯模型与改进的光流场跟踪算法结合的方 法,实现了复杂背景下实时的手势跟踪,具有快速和准确的特点,且具有较好的鲁棒性．对于动态手势识别器,采 用了隐马尔可夫模型（HMM）作为训练识别算法．考虑到动态手势特征本身的一些特点,对HMM 参数优化算法重 估式加以修正,调整了算法比例因子,从而推导了最佳状态链的确定算法、HMM 参数优化算法．最后将研究开发 的动态手势识别算法成功地应用到了基于网络的远程机器人控制系统中．     

基于一种改进禁忌搜索算法优化离散隐马尔可夫模型

隐马尔可夫模型(HMM,HiddenMarkovModel)是语音识别和手势识别中广泛使用的统计模式识别方法。文章提出了一种改进的禁忌搜索(ITS,ImprovedTabuSearch)优化HMM的参数。传统的TabuSearch(TS)与局部搜索算法(极大似然法)交替进行,从而加快了算法的收敛速度,并得到优化解。分别用TS及ITS训练隐马尔可夫模型进行动态手势识别。结果表明ITS可获得更高的识别率,且能达到全局优化。     

基于条件随机域的上下文人类动作识别

提出一种新的基于条件随机域和隐马尔可夫模型（HMM）的人类动作识别方法——HMCRF。目前已有的动作识别方法均使用隐马尔可夫模型及其变型,这些模型一个最突出的不足就是要求观察值相互独立。条件模型很容易表示上下文相关性,且可使用动态规划做到有效且精确的推论,它的参数可以通过凸函数优化训练得到。把条件图形模型应用于动作识别之上,并通过大量的实验表明,所提出的方法在识别正确率方面明显优于一般线性结构的CRF和HMM。     

Zero knowledge hidden Markov model inference

Hidden Markov models (HMMs) are widely used in pattern recognition. HMM construction requires an initial model structure that is used as a starting point to estimate the model’s parameters. To construct a HMM without a priori knowledge of the structure, we use an approach developed by Crutchfield and Shalizi that requires only a sequence of observations and a maximum data window size. Values of the maximum data window size that are too small result in incorrect models being constructed. Values that are too large reduce the number of data samples that can be considered and exponentially increase the algorithm’s computational complexity. In this paper, we present a method for automatically inferring this parameter directly from training data as part of the model construction process. We present theoretical and experimental results that confirm the utility of the proposed extension.     

Ice hockey shooting event modeling with mixture hidden Markov model

In this paper we present a new event analysis framework based on mixture hidden Markov model (HMM) for ice hockey videos. Hockey is a competitive sport and hockey videos are hard to analyze because of the homogeneity of its frame features. However, the temporal dynamics of hockey videos is highly structured. Using the mixture representation of local observations and Markov chain property of hockey event structure, we successfully model the hockey event as a mixture HMM. Based on the mixture HMM, the hockey event could be classified with high accuracy. Two types of mixture HMMs, Gaussian mixture and independent component analysis (ICA) mixture, are compared for the hockey video event classification. The results confirm our analysis that the mixture HMM is a suitable model to deal with videos with intensive activities. The new mixture HMM hockey event model could be a very useful tool for hockey game analysis.     

Feature Enhancement for Noisy Speech Recognition With a Time-Variant Linear Predictive HMM Structure

This paper presents a new approach for speech feature enhancement in the log-spectral domain for noisy speech recognition. A switching linear dynamic model (SLDM) is explored as a parametric model for the clean speech distribution. Each multivariate linear dynamic model (LDM) is associated with the hidden state of a hidden Markov model (HMM) as an attempt to describe the temporal correlations among adjacent frames of speech features. The state transition on the Markov chain is the process of activating a different LDM or activating some of them simultaneously by different probabilities generated by the HMM. Rather than holding a transition probability for the whole process, a connectionist model is employed to learn the time variant transition probabilities. With the resulting SLDM as the speech model and with a model for the noise, speech and noise are jointly tracked by means of switching Kalman filtering. Comprehensive experiments are carried out using the Aurora2 database to evaluate the new algorithm. The results show that the new SLDM approach can further improve the speech feature enhancement performance in terms of noise-robust recognition accuracy, since the transition probabilities among the LDMs can be described more precisely at each time point.     

Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

This paper is concerned with model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples.     

Optimal sensor scheduling for hidden Markov model state estimation

Consider the Hidden Markov model where the realization of a single Markov chain is observed by a number of noisy sensors. The sensor scheduling problem for the resulting hidden Markov model is as follows: design an optimal algorithm for selecting at each time instant, one of the many sensors to provide the next measurement. Each measurement has an associated measurement cost. The problem is to select an optimal measurement scheduling policy, so as to minimize a cost function of estimation errors and measurement costs. The problem of determining the optimal measurement policy is solved via stochastic dynamic programming. Numerical results are presented.     

Modeling the dynamic optimal advertising in stochastic condition

An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales reponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulated. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.     

A new approach based on a discrete hidden Markov model using the Rocchio algorithm for the diagnosis of heart valve diseases

Abstract: Application of the Doppler ultrasound technique in the diagnosis of heart diseases has been increasing in the last decade since it is non‐invasive, practicable and reliable. In this study, a new approach based on the discrete hidden Markov model (DHMM) is proposed for the diagnosis of heart valve disorders. For the calculation of hidden Markov model (HMM) parameters according to the maximum likelihood approach, HMM parameters belonging to each class are calculated by using training samples that only belong to their own classes. In order to calculate the parameters of DHMMs, not only training samples of the related class but also training samples of other classes are included in the calculation. Therefore HMM parameters that reflect a class's characteristics are more represented than other class parameters. For this aim, the approach was to use a hybrid method by adapting the Rocchio algorithm. The proposed system was used in the classification of the Doppler signals obtained from aortic and mitral heart valves of 215 subjects. The performance of this classification approach was compared with the classification performances in previous studies which used the same data set and the efficiency of the new approach was tested. The total classification accuracy of the proposed approach (95.12%) is higher than the total accuracy rate of standard DHMM (94.31%), continuous HMM (93.5%) and support vector machine (92.67%) classifiers employed in our previous studies and comparable with the performance levels of classifications using artificial neural networks (95.12%) and fuzzy‐C‐means/CHMM (95.12%).     

Stochastic control of two partially observed competing queues

We consider the dynamic control of two queues competing for the services of one server. The problem is to design a server time allocation strategy, when the sizes of the queues are not observable. The performance criterion used is total expected aggregate delay. The server is assumed to observe arrivals but not departures. This problem is formulated as a stochastic optimal control problem with partial observations. The framework we adopt is that of stochastic control in discrete time and countable "state space." The observations are modeled as discrete time, 0-1 point processes with rates that are influenced by a Markov chain. Examples from computer control of urban traffic are given, to illustrate the practical motivation behind the present work, and to relate to earlier work by us on the subject. A particular feature of the formulation is that the observations are influenced by transitions of the state of the Markov chain. The classical tools of simple Bayes rule and dynamic programming suffice for the analysis. In particular, we show that the "one step" predicted density for the state of the Markov chain, given the point process observations is a sufficient statistic for control. This framework is then applied to the specific problem of two queues competing for the services of one server. We obtain explicit solutions for the finite time expected aggregate delay problem. The implications of these results for practical applications as well as implementation aspects of the resulting optimal control laws are discussed.     

A novel approach to equipment health management based on auto-regressive hidden semi-Markov model （AR-HSMM）

As a new maintenance method, CBM （condition based maintenance） is becoming more and more important for the health management of complicated and costly equipment. A prerequisite to widespread deployment of CBM technology and prac- tice in industry is effective diagnostics and prognostics. Recently, a pattern recog- nition technique called HMM （hidden Markov model） was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equip- ment health management based on auto-regressive hidden semi-Markov model （AR-HSMM）. Compared with HMM, AR-HSMM has three advantages： 1） It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2） It can relax observations＇ independence assumption by accom- modating a link between consecutive observations. 3） It does not follow the unre- alistic Markov chain＇s memoryless assumption and therefore provides more pow- erful modeling and analysis capability for real problems. To facilitate the computa- tion in the proposed AR-HSMM-based diagnostics and prognostics, new forward- backward variables are defined and a modified forward-backward algorithm is de- veloped. The evaluation of the proposed methodology was carried out through a real world application case study： health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decision- making in equipment health management.     

The Impact of Short-Sale Constraints on Asset Allocation Strategies via the Backward Markov Chain Approximation Method

This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuous-time stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be obtained analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the impact of short-sale constraints on asset allocation decisions. Our results show that the short-sale constraints do indeed have a significant impact on these decisions.