Factorial hidden Markov models and the generalized backfitting algorithm

Previous researchers developed new learning architectures for sequential data by extending conventional hidden Markov models through the use of distributed state representations. Although exact inference and parameter estimation in these architectures is computationally intractable, Ghahramani and Jordan (1997) showed that approximate inference and parameter estimation in one such architecture, factorial hidden Markov models (FHMMs), is feasible in certain circumstances. However, the learning algorithm proposed by these investigators, based on variational techniques, is difficult to understand and implement and is limited to the study of real-valued data sets. This chapter proposes an alternative method for approximate inference and parameter estimation in FHMMs based on the perspective that FHMMs are a generalization of a well-known class of statistical models known as generalized additive models (GAMs; Hastie & Tibshirani, 1990). Using existing statistical techniques for GAMs as a guide, we have developed the generalized backfitting algorithm. This algorithm computes customized error signals for each hidden Markov chain of an FHMM and then trains each chain one at a time using conventional techniques from the hidden Markov models literature. Relative to previous perspectives on FHMMs, we believe that the viewpoint taken here has a number of advantages. First, it places FHMMs on firm statistical foundations by relating them to a class of models that are well studied in the statistics community, yet it generalizes this class of models in an interesting way. Second, it leads to an understanding of how FHMMs can be applied to many different types of time-series data, including Bernoulli and multinomial data, not just data that are real valued. Finally, it leads to an effective learning procedure for FHMMs that is easier to understand and easier to implement than existing learning procedures. Simulation results suggest that FHMMs trained with the generalized backfitting algorithm are a practical and powerful tool for analyzing sequential data.     

Hierarchical multi-channel hidden semi Markov graphical models for activity recognition

Recognizing human actions from a stream of unsegmented sensory observations is important for a number of applications such as surveillance and human-computer interaction. A wide range of graphical models have been proposed for these tasks, and are typically extensions of the generative hidden Markov models (HMMs) or their discriminative counterpart, conditional random fields (CRFs). These extensions typically address one of three key limitations in the basic HMM/CRF formalism – unrealistic models for the duration of a sub-event, not encoding interactions among multiple agents directly and not modeling the inherent hierarchical organization of activities. In our work, we present a family of graphical models that generalize such extensions and simultaneously model event duration, multi agent interactions and hierarchical structure. We also present general algorithms for efficient learning and inference in such models based on local variational approximations. We demonstrate the effectiveness of our framework by developing graphical models for applications in automatic sign language (ASL) recognition, and for gesture and action recognition in videos. Our methods show results comparable to state-of-the-art in the datasets we consider, while requiring far fewer training examples compared to low-level feature based methods.     

Dance performance evaluation using hidden Markov models

We present in this paper a hidden Markov model‐based system for real‐time gesture recognition and performance evaluation. The system decodes performed gestures and outputs at the end of a recognized gesture, a likelihood value that is transformed into a score. This score is used to evaluate a performance comparing to a reference one. For the learning procedure, a set of relational features has been extracted from high‐precision motion capture system and used to train hidden Markov models. At runtime, a low‐cost sensor (Microsoft Kinect) is used to capture a learner's movements. An intermediate step of model adaptation was hence requested to allow recognizing gestures captured by this low‐cost sensor. We present one application of this gesture evaluation system in the context of traditional dance basics learning. The estimation of the log‐likelihood allows giving a feedback to the learner as a score related to his performance. Copyright © 2016 John Wiley & Sons, Ltd.     

Minimum classification error learning for sequential data in the wavelet domain

Wavelet analysis has found widespread use in signal processing and many classification tasks. Nevertheless, its use in dynamic pattern recognition have been much more restricted since most of wavelet models cannot handle variable length sequences properly. Recently, composite hidden Markov models which observe structured data in the wavelet domain were proposed to deal with this kind of sequences. In these models, hidden Markov trees account for local dynamics in a multiresolution framework, while standard hidden Markov models capture longer correlations in time. Despite these models have shown promising results in simple applications, only generative approaches have been used so far for parameter estimation. The goal of this work is to take a step forward in the development of dynamic pattern recognizers using wavelet features by introducing a new discriminative training method for this Markov models. The learning strategy relies on the minimum classification error approach and provides re-estimation formulas for fully non-tied models. Numerical experiments on phoneme recognition show important improvement over the recognition rate achieved by the same models trained using maximum likelihood estimation.     

A multiscale edge detection algorithm based on wavelet domain vector hidden Markov tree model

The wavelet analysis is an efficient tool for the detection of image edges. Based on the wavelet analysis, we present an unsupervised learning algorithm to detect image edges in this paper. A wavelet domain vector hidden Markov tree (WD-VHMT) is employed in our algorithm to model the statistical properties of multiscale and multidirectional (subband) wavelet coefficients of an image. With this model, each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge. The WD-VHMT model can be learned by an expectation-maximization algorithm. After the model is learned, we employ an extended Viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation. The experiment results of the edge detection for several images are provided to evaluate our algorithm.     

双层隐马尔可夫链的突发流合成

网络流模型被广泛用于构建网络与网络服务的测试环境,其准确性直接影响各种业务的性能评估结果及在实际网络环境中的鲁棒性.随着电子商务及新型网络应用的普及,突发流现象已经成为现代互联网的主要特征之一.针对平稳网络流而设计的传统网络流模型已经难以有效地描述现代网络中突发流的时间结构性及统计属性,从而不能准确反映现代网络流的行为特征.为此,提出一种新的结构化双层隐马尔可夫模型用于模拟实际网络环境下的突发流,并设计了有效的模型参数推断算法及突发流合成方法.该模型通过结构化的2层隐马尔可夫过程描述突发流并实现仿真合成,使合成流可以重现实际突发流的时间结构性、统计特性及自相似性.实验表明,该模型可以有效合成突发流.     

A self-growing hidden Markov tree for wafer map inspection

This paper presents an automatic identification of the defect spatial wafer map using a growing wavelet-based hidden Markov tree (gHMT) statistical model. The hierarchical tree-based model, gHMT, utilizes the growing and learning procedure to increase successively the size of the wavelet tree. It can characterize image processing masks from the defect spatial patterns. Like the standard hidden Markov tree, gHMT cannot only capture the statistical behavior of the real-world measurements at multiple scales in space and frequency but also has the ability to accurately identify the locations of the defect regions using the smallest possible size. These regions provide essential information and intrinsic features of each pattern. When all the possible defect patterns are modeled by gHMT, the maximum likelihood classifier is applied to the wavelet energy features extracted from each trained models. Accordingly, defect spatial patterns are identified. The effectiveness of the proposed classifier based on gHMT is illustrated through the experimental data from a wafer foundry plant. It can identify different defect patterns on wafers to help readers delve into the matter.     

Writer identification of Chinese handwriting documents using hidden Markov tree model

Handwriting-based writer identification, a branch of biometrics, is an active research topic in pattern recognition. Since most existing methods and models aim to on-line and/or text-dependent writer identification, it is necessary to propose new methods for off-line, text-independent writer identification. At present, two-dimensional Gabor model is widely acknowledged as an effective and classic method for off-line, text-independent handwriting identification, while it still suffers from some inherent shortcomings, such as the excessive calculational cost. In this paper, we present a novel method based on hidden Markov tree (HMT) model in wavelet domain for off-line, text-independent writer identification of Chinese handwriting documents. Our experiments show this HMT method, compared with two-dimensional Gabor model, not only achieves better identification results but also greatly reduces the elapsed time on computation.     

Bayesian event detection for sport games with hidden Markov model

Event detection can be defined as the problem of detecting when a target event has occurred, from a given data sequence. Such an event detection problem can be found in many fields in science and engineering, such as signal processing, pattern recognition, and image processing. In recent years, many data sequences used in these fields, especially in video data analysis, tend to be high dimensional. In this paper, we propose a novel event detection method for high-dimensional data sequences in soccer video analysis. The proposed method assumes a Bayesian hidden Markov model with hyperparameter learning in addition to the parameter leaning. This is in an attempt to reduce undesired influences from ineffective components within the high-dimensional data. Implemention is performed by Markov Chain Monte Carlo. The proposed method was tested against an event detection problem with sequences of 40-dimensional feature values extracted from real professional soccer games. The algorithm appears functional.     

Recognition of DNA gene fragments using hidden Markov models

A model of the recognition of functional sites of genes in DNA on the basis of hidden Markov models is considered. It is shown how algorithms based on Markov chain models of various orders can be used to detect fragments of genes of three genomes of higher organisms.     

Rotation and gray scale transform invariant texture identificationusing wavelet decomposition and hidden Markov model

In this correspondence, we have presented a rotation and gray scale transform invariant texture recognition scheme using the combination of quadrature mirror filter (QMF) bank and hidden Markov model (HMM). In the first stage, the QMF bank is used as the wavelet transform to decompose the texture image into subbands. The gray scale transform invariant features derived from the statistics based on first-order distribution of gray levels are then extracted from each subband image. In the second stage, the sequence of subbands is modeled as a hidden Markov model (HMM), and one HMM is designed for each class of textures. The HMM is used to exploit the dependence among these subbands, and is able to capture the trend of changes caused by rotation. During recognition, the unknown texture is matched against all the models. The best matched model identifies the texture class. Up to 93.33% classification accuracy is reported     

Learning Atomic Human Actions Using Variable-Length Markov Models

Visual analysis of human behavior has generated considerable interest in the field of computer vision because of its wide spectrum of potential applications. Human behavior can be segmented into atomic actions, each of which indicates a basic and complete movement. Learning and recognizing atomic human actions are essential to human behavior analysis. In this paper, we propose a framework for handling this task using variable-length Markov models (VLMMs). The framework is comprised of the following two modules: a posture labeling module and a VLMM atomic action learning and recognition module. First, a posture template selection algorithm, based on a modified shape context matching technique, is developed. The selected posture templates form a codebook that is used to convert input posture sequences into discrete symbol sequences for subsequent processing. Then, the VLMM technique is applied to learn the training symbol sequences of atomic actions. Finally, the constructed VLMMs are transformed into hidden Markov models (HMMs) for recognizing input atomic actions. This approach combines the advantages of the excellent learning function of a VLMM and the fault-tolerant recognition ability of an HMM. Experiments on realistic data demonstrate the efficacy of the proposed system.     

Speech recognition with continuous-parameter hidden Markov models

The acoustic modeling problem in automatic speech recognition is examined from an information-theoretic point of view. This problem is to design a speech-recognition system which can extract from the speech waveform as much information as possible about the corresponding word sequence. The information extraction process is broken down into two steps: a signal-processing step which converts a speech waveform into a sequence of information-bearing acoustic feature vectors, and a step which models such a sequence. We are primarily concerned with the use of hidden Markov models to model sequences of feature vectors which lie in a continuous space. We explore the trade-off between packing information into such sequences and being able to model them accurately. The difficulty of developing accurate models of continuous-parameter sequences is addressed by investigating a method of parameter estimation which is designed to cope with inaccurate modeling assumptions.     

Generalized hidden Markov models. I. Theoretical frameworks

In this paper, we present the theoretical framework for the generalization of classical hidden Markov models using fuzzy measures and fuzzy integrals. The main characteristic of the generalization is the relaxation of the usual additivity constraint of probability measures. Fuzzy integrals are defined with respect to fuzzy measures, whose key property is monotonicity with respect to set inclusion. This property is far weaker than the usual additivity property of probability measures. As a result of the new formulation, the statistical independence assumption of the classical hidden Markov models is relaxed. Two attractive properties of this generalization are: the generalized hidden Markov model reduces to the classical hidden Markov model if we used the Choquet fuzzy integral and probability measures; and the establishment of a relation between the generalized hidden Markov model and the classical nonstationary hidden Markov model in which the transitional parameters vary with time     

A reservoir-driven non-stationary hidden Markov model

In this work, we propose a novel approach towards sequential data modeling that leverages the strengths of hidden Markov models and echo-state networks (ESNs) in the context of non-parametric Bayesian inference approaches. We introduce a non-stationary hidden Markov model, the time-dependent state transition probabilities of which are driven by a high-dimensional signal that encodes the whole history of the modeled observations, namely the state vector of a postulated observations-driven ESN reservoir. We derive an efficient inference algorithm for our model under the variational Bayesian paradigm, and we examine the efficacy of our approach considering a number of sequential data modeling applications.     

Diagnostic tools for evaluating and updating hidden Markov models

In this paper we consider two related problems in hidden Markov models (HMMs). One, how the various parameters of an HMM actually contribute to predictions of state sequences and spatio-temporal pattern recognition. Two, how the HMM parameters (and associated HMM topology) can be updated to improve performance. These issues are examined in the context of four different experimental settings from pure simulations to observed data. Results clearly demonstrate the benefits of applying some critical tests on the model parameters before using it as a predictor or spatio-temporal pattern recognition technique.     

基于隐马尔可夫模型的运动目标轨迹识别 *

引入改进的隐马尔可夫模型算法,针对真实场景中运动目标轨迹的复杂程度对各个轨迹模式类建立相应的隐马尔可夫模型,利用训练样本训练模型得到可靠的模型参数;计算测试样本对于各个模型的最大似然概率,选取最大概率值对应的轨迹模式类作为轨迹识别的结果,对两种场景中聚类后的轨迹进行训练与识别。实验结果表明,平均识别率分别达到87.76 %和94. 19%。     

Audio-visual human recognition using semi-supervised spectral learning and hidden Markov models

This paper presents a multimodal system for reliable human identity recognition under variant conditions. Our system fuses the recognition of face and speech with a general probabilistic framework. For face recognition, we propose a new spectral learning algorithm, which considers not only the discriminative relations among the training data but also the generative models for each class. Due to the tedious cost of face labeling in practice, our spectral face learning utilizes a semi-supervised strategy. That is, only a small number of labeled faces are used in our training step, and the labels are optimally propagated to other unlabeled training faces. Besides requiring much less labeled data, our algorithm also enables a natural way to explicitly train an outlier model that approximately represents unauthorized faces. To boost the robustness of our system for human recognition under various environments, our face recognition is further complemented by a speaker identification agent. Specifically, this agent models the statistical variations of fixed-phrase speech using speaker-dependent word hidden Markov models. Experiments on benchmark databases validate the effectiveness of our face recognition and speaker identification agents, and demonstrate that the recognition accuracy can be apparently improved by integrating these two independent biometric sources together.     

Modeling and recognition of cursive words with hidden Markov models

In this paper, a new method for modeling and recognizing cursive words with hidden Markov models (HMM) is presented. In the proposed method, a sequence of thin fixed-width vertical frames are extracted from the image, capturing the local features of the handwriting. By quantizing the feature vectors of each frame, the input word image is represented as a Markov chain of discrete symbols. A handwritten word is regarded as a sequence of characters and optional ligatures. Hence, the ligatures are also explicitly modeled. With this view, an interconnection network of character and ligature HMMs is constructed to model words of indefinite length. This model can ideally describe any form of handwritten words, including discretely spaced words, pure cursive words and unconstrained words of mixed styles. Experiments have been conducted with a standard database to evaluate the performance of the overall scheme. The performance of various search strategies based on the forward and backward score has been compared. Experiments on the use of a preclassifier based on global features show that this approach may be useful for even large-vocabulary recognition tasks.