Hidden Markov models with factored Gaussian mixtures densities

We present a factorial representation of Gaussian mixture models for observation densities in hidden Markov models (HMMs), which uses the factorial learning in the HMM framework. We derive the reestimation formulas for estimating the factorized parameters by the Expectation Maximization (EM) algorithm and propose a novel method for initializing them. To compare the performances of the proposed models with that of the factorial hidden Markov models and HMMs, we have carried out extensive experiments which show that this modelling approach is effective and robust.     

Type-2 fuzzy Gaussian mixture models

This paper presents a new extension of Gaussian mixture models (GMMs) based on type-2 fuzzy sets (T2 FSs) referred to as T2 FGMMs. The estimated parameters of the GMM may not accurately reflect the underlying distributions of the observations because of insufficient and noisy data in real-world problems. By three-dimensional membership functions of T2 FSs, T2 FGMMs use footprint of uncertainty (FOU) as well as interval secondary membership functions to handle GMMs uncertain mean vector or uncertain covariance matrix, and thus GMMs parameters vary anywhere in an interval with uniform possibilities. As a result, the likelihood of the T2 FGMM becomes an interval rather than a precise real number to account for GMMs uncertainty. These interval likelihoods are then processed by the generalized linear model (GLM) for classification decision-making. In this paper we focus on the role of the FOU in pattern classification. Multi-category classification on different data sets from UCI repository shows that T2 FGMMs are consistently as good as or better than GMMs in case of insufficient training data, and are also insensitive to different areas of the FOU. Based on T2 FGMMs, we extend hidden Markov models (HMMs) to type-2 fuzzy HMMs (T2 FHMMs). Phoneme classification in the babble noise shows that T2 FHMMs outperform classical HMMs in terms of the robustness and classification rate. We also find that the larger area of the FOU in T2 FHMMs with uncertain mean vectors performs better in classification when the signal-to-noise ratio is lower.     

Dynamic classification of ballistic missiles using neural networks and hidden Markov models

This paper addresses dynamic classification of different ranges of ballistic missiles (BM) for air defense application based on kinematic attributes acquired by radars for taking appropriate measures to intercept them. The problem of dynamic classification is formulated using real-time neural network (RTNN) and hidden Markov model (HMM). The idea behind these algorithms is to calculate the output in one pass rather than training and computing over large number of iterations. Besides, to meet the conflicting requirements of classifying small as well as long-range trajectories, we are also proposing a formulation for partitioning the trajectory by using moving window concept. This concept allows us to use parameters in localized frame which helps in handling wide-range of trajectories to fit into the same network. These algorithms are evaluated using the simulated data generated from 6 degree-of-freedom (6DOF) mathematical model, which models missile trajectories. Experimental results show that both the networks are classifying above 95% with real-time neural network outperforming HMM in terms of time of computation on same data. The small classification time enables the use of real-time classification neural network in complex scenario of multi-radar, multi-target engagement by interceptor missiles. To the best of our knowledge this is the first time an attempt is made to classify ballistic missiles using RTNN and HMM.     

Similarity-based classification of sequences using hidden Markov models

Hidden Markov models (HMM) are a widely used tool for sequence modelling. In the sequence classification case, the standard approach consists of training one HMM for each class and then using a standard Bayesian classification rule. In this paper, we introduce a novel classification scheme for sequences based on HMMs, which is obtained by extending the recently proposed similarity-based classification paradigm to HMM-based classification. In this approach, each object is described by the vector of its similarities with respect to a predetermined set of other objects, where these similarities are supported by HMMs. A central problem is the high dimensionality of resulting space, and, to deal with it, three alternatives are investigated. Synthetic and real experiments show that the similarity-based approach outperforms standard HMM classification schemes.     

Learning mixture models with support vector machines for sequence classification and segmentation

This paper focuses on learning recognition systems able to cope with sequential data for classification and segmentation tasks. It investigates the integration of discriminant power in the learning of generative models, which are usually used for such data. Based on a procedure that transforms a sample data into a generative model, learning is viewed as the selection of efficient component models in a mixture of generative models. This may be done through the learning of a support vector machine. We propose a few kernels for this and report experimental results for classification and segmentation tasks.     

Masquerade detection using profile hidden Markov models

In this paper, we consider the problem of masquerade detection, based on user-issued UNIX commands. We present a novel detection technique based on profile hidden Markov models (PHMMs). For comparison purposes, we implement an existing modeling technique based on hidden Markov models (HMMs). We compare these approaches and show that, in general, our PHMM technique is competitive with HMMs. However, the standard test data set lacks positional information. We conjecture that such positional information would give our PHMM a significant advantage over HMM-based detection. To lend credence to this conjecture, we generate a simulated data set that includes positional information. Based on this simulated data, experimental results show that our PHMM-based approach outperforms other techniques when limited training data is available.     

Almost sure parameter estimation and convergence rates for hidden Markov models

A continuous-time version of Kronecker's Lemma is established and used to give rates of convergence for parameter estimates in hidden Markov models.     

Handwritten word-spotting using hidden Markov models and universal vocabularies

Handwritten word-spotting is traditionally viewed as an image matching task between one or multiple query word-images and a set of candidate word-images in a database. This is a typical instance of the query-by-example paradigm. In this article, we introduce a statistical framework for the word-spotting problem which employs hidden Markov models (HMMs) to model keywords and a Gaussian mixture model (GMM) for score normalization. We explore the use of two types of HMMs for the word modeling part: continuous HMMs (C-HMMs) and semi-continuous HMMs (SC-HMMs), i.e. HMMs with a shared set of Gaussians. We show on a challenging multi-writer corpus that the proposed statistical framework is always superior to a traditional matching system which uses dynamic time warping (DTW) for word-image distance computation. A very important finding is that the SC-HMM is superior when labeled training data is scarce—as low as one sample per keyword—thanks to the prior information which can be incorporated in the shared set of Gaussians.     

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.     

Object classification by fusing SVMs and Gaussian mixtures

We present a new technique that employs support vector machines (SVMs) and Gaussian mixture densities (GMDs) to create a generative/discriminative object classification technique using local image features. In the past, several approaches to fuse the advantages of generative and discriminative approaches were presented, often leading to improved robustness and recognition accuracy. Support vector machines are a well known discriminative classification framework but, similar to other discriminative approaches, suffer from a lack of robustness with respect to noise and overfitting. Gaussian mixtures, on the contrary, are a widely used generative technique. We present a method to directly fuse both approaches, effectively allowing to fully exploit the advantages of both. The fusion of SVMs and GMDs is done by representing SVMs in the framework of GMDs without changing the training and without changing the decision boundary. The new classifier is evaluated on the PASCAL VOC 2006 data. Additionally, we perform experiments on the USPS dataset and on four tasks from the UCI machine learning repository to obtain additional insights into the properties of the proposed approach. It is shown that for the relatively rare cases where SVMs have problems, the combined method outperforms both individual ones.     

Image denoising in extended Shearlet domain using hidden Markov tree models

Denoising of images is one of the most basic tasks of image processing. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. In this paper, a new image denoising approach in extended Shearlet domain using hidden Markov tree (HMT) model is proposed. Firstly, the joint statistics and mutual information of the extended DST coefficients are studied. Then, the extended DST coefficients are modeled using an HMT model with Gaussian mixtures, which can effectively capture the intra-scale and inter-scale dependencies. Finally, the extended Shearlet HMT model is applied to image denoising. Extensive experimental results demonstrate that our extended Shearlet HMT denoising method can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.     

A comparative evaluation of neural networks and hidden Markov models for monitoring turning tool wear

Condition monitoring of machine tool inserts is important for increasing the reliability and quality of machining operations. Various methods have been proposed for effective tool condition monitoring (TCM), and currently it is generally accepted that the indirect sensor-based approach is the best practical solution to reliable TCM. Furthermore, in recent years, neural networks (NNs) have been shown to model successfully, the complex relationships between input feature sets of sensor signals and tool wear data. NNs have several properties that make them ideal for effectively handling noisy and even incomplete data sets. There are several NN paradigms which can be combined to model static and dynamic systems. Another powerful method of modeling noisy dynamic systems is by using hidden Markov models (HMMs), which are commonly employed in modern speech-recognition systems. The use of HMMs for TCM was recently proposed in the literature. Though the results of these studies were quite promising, no comparative results of competing methods such as NNs are currently available. This paper is aimed at presenting a comparative evaluation of the performance of NNs and HMMs for a TCM application. The methods are employed on exactly the same data sets obtained from an industrial turning operation. The advantages and disadvantages of both methods are described, which will assist the condition-monitoring community to choose a modeling method for other applications.     

A two-stage mechanism for registration and classification of ECG using Gaussian mixture model

An automatic classifier for electrocardiogram (ECG) based cardiac abnormality detection using Gaussian mixture model (GMM) is presented here. In first stage, pre-processing that includes re-sampling, QRS detection, linear prediction (LP) model estimation, residual error signal computation and principal component analysis (PCA) has been used for registration of linearly independent ECG features. GMM is here used for classification based on the registered features in a two-class pattern classification problem using 730 ECG segments from MIT-BIH Arrhythmia and European ST-T Ischemia datasets. A set of 12 features explaining 99.7% of the data variability is obtained using PCA from residual error signals for GMM based classification. Sixty percent of the data is used for training the classifier and 40% for validating. It is observed that the overall accuracy of the proposed strategy is 94.29%. As an advantage, it is also verified that Chernoff bound and Bhattacharya bounds lead to minimum error for GMM based classifier. In addition, a comparative study is done with the standard classification techniques with respect to its overall accuracy.     

Links between probabilistic automata and hidden Markov models: probability distributions, learning models and induction algorithms

This article presents an overview of Probabilistic Automata (PA) and discrete Hidden Markov Models (HMMs), and aims at clarifying the links between them. The first part of this work concentrates on probability distributions generated by these models. Necessary and sufficient conditions for an automaton to define a probabilistic language are detailed. It is proved that probabilistic deterministic automata (PDFA) form a proper subclass of probabilistic non-deterministic automata (PNFA). Two families of equivalent models are described next. On one hand, HMMs and PNFA with no final probabilities generate distributions over complete finite prefix-free sets. On the other hand, HMMs with final probabilities and probabilistic automata generate distributions over strings of finite length. The second part of this article presents several learning models, which formalize the problem of PA induction or, equivalently, the problem of HMM topology induction and parameter estimation. These learning models include the PAC and identification with probability 1 frameworks. Links with Bayesian learning are also discussed. The last part of this article presents an overview of induction algorithms for PA or HMMs using state merging, state splitting, parameter pruning and error-correcting techniques.     

Perception-based hidden Markov models: a theoretical framework for data mining and knowledge discovery

 The combination of objective measurements and human perceptions using hidden Markov models with particular reference to sequential data mining and knowledge discovery is presented in this paper. Both human preferences and statistical analysis are utilized for verification and identification of hypotheses as well as detection of hidden patterns. As another theoretical view, this work attempts to formalize the complementarity of the computational theories of hidden Markov models and perceptions for providing solutions associated with the manipulation of the internet.     

Combination of wavelet and SIFT features for image classification using trained Gaussian mixture model

This paper presents an effective combination of Wavelet-based features and SIFT features. For the combined feature patches extracted from images we then adopt the PCA transformation to reduce the dimensionality of their feature vectors. And the reduced vectors are used to train Gaussian Mixture Models （GMMs） in which the mixture weights and Gaussian parameters are updated iteratively. We performed the method on Caltech datasets and compared the results with several other methods. It shown that the combination of salient feature vectors and GMM gives a much better improvement in image classification.