Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical structure and hence can form the theoretical basis for use in a wide range of applications. Sec-ond the models, when applied properly, work very well in practice for several important applications. In this paper we attempt to care-fully and methodically review the theoretical aspects of this type of statistical modeling and show how they have been applied to selected problems in machine recognition of speech. I.

Parameter sharing plays an important role in statistical modeling since training data are usually limited. On the one hand, we would like to use models that are as detailed as possible. On the other hand, with models too detailed, we can no longer reliably estimate the parameters. Triphone generalization may force two models to be merged together when only parts of the model output distributions are similar, while the rest of the output distributions are different. This problem can be avoided if clustering is carried out at the distribution level. In this paper, a shared-distribution model is proposed to replace generalized triphone models for speaker-independent continuous speech recognition. Here, output distributions in the hidden Markov model are shared with each other if they exhibit acoustic similarity. In addition to detailed representation, it also gives us the freedom to use a large number of states for each phonetic model. Although an increase in the number of states will inc...

This paper discusses a probabilistic model-based approach to clustering sequences, using hidden Markov models (HMMs). The problem can be framed as a generalization of the standard mixture model approach to clustering in feature space. Two primary issues are addressed. First, a novel parameter initialization procedure is proposed, and second, the more difficult problem of determining the number of clusters K, from the data, is investigated. Experimental results indicate that the proposed techniques are useful for revealing hidden cluster structure in data sets of sequences. 1 Introduction Consider a data set D consisting of N sequences, D = fS 1 ; . . . ; SN g. S i = (x i 1 ; . . . x i L i ) is a sequence of length L i composed of potentially multivariate feature vectors x. The problem addressed in this paper is the discovery from data of a natural grouping of the sequences into K clusters. This is analagous to clustering in multivariate feature space which is normally handled by m...

Automatic music classification is essential for implementing efficient music information retrieval systems; meanwhile, it may shed light on the process of human’s music perception. This paper describes our work on the classification of folk music from different countries based on their monophonic melodies using hidden Markov models. Music corpora of Irish, German and Austrian folk music in various symbolic formats were used as the data set. Different representations and HMM structures were tested and compared. The classification performances achieved 75%, 77 % and 66 % for 2-way classifications and 63 % for 3-way classification using 6-state left-right HMM with the interval representation in the experiment. This shows that the melodies of folk music do carry some statistical features to distinguish them. We expect that the result will improve if we use a more discriminable data set and the approach should be applicable to other music classification tasks and acoustic musical signals. Furthermore, the results suggest to us a new way to think about musical style similarity.

Model-based clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic model-based clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing model-based clustering algorithms. In this view, clusters are represented as probabilistic models in a model space that is conceptually separate from the data space. For partitional clustering, the view is conceptually similar to the ExpectationMaximization (EM) algorithm. For hierarchical clustering, the graph-based view helps to visualize critical/important distinctions between similarity-based approaches and model-based approaches.

In large-vocabulary speech recognition, the decoder often encounters triphones that are not covered in the training data. These unseen triphones are usually represented by corresponding diphones or context independent monophones. We propose to use decision-tree based senones to generate needed senonic baseforms for unseen triphones. A decision tree is built for each individual Markov state of each phone, and the leaves of the trees constitute the senone codebook. To find the senone a Markov state of any triphone is associated with, we traverse the corresponding tree until we reach a leaf node, where a senone is represented. We used the DARPA 5,000-word speaker-independent Wall Street Journal dictation task to evaluate the proposed method. The word error rate was reduced by 11% when unseen triphones were modeled by the decision-tree based senones. When there were at least 5 unseen triphones in each test utterance, the error rate could be reduced by more than 20%. This research was spons...

A new statistical model for characterizing texture images based on wavelet-domain hidden Markov models and steerable pyramids is presented. The new model is shown to capture well both the subband marginal distributions and the dependencies across scales and orientations of the wavelet descriptors. Once it is trained for an input texture image, the model can be easily steered to characterize that texture at any other orientation. After a diagonalization operation, one obtains a rotation-invariant model of the texture image. The effectiveness of the new texture models are demonstrated in retrieval experiments with large image databases, where significant performance gains are shown. Keywords texture characterization, image retrieval, rotation invariance, wavelets, hidden Markov models, steerable pyramids. Corresponding author. Address: see above; Phone: +41 21 693 7663; Fax: +41 21 693 4312. y Also with Department of EECS, UC Berkeley, Berkeley CA 94720, USA. April 23, 2001 DRAFT I.

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications. 1.

Hidden Markov models (hmms) and partially observable Markov decision processes (pomdps) provide a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office buildings, which are typical for robot navigation and planning. The work presented here describes a formal framework for incorporating readily available odometric information into both the models and the algorithm that learns them. By taking advantage of such information, learning hmms/pomdps can be made better and require fewer iterations, while being robust in the face of data reduction. That is, the performance of our algorithm does not significantly deteriorate as the training sequences provided to it become significantly shorter. Formal proofs for the convergence of the algorithm to a local maximum of the likelihood function are provided. Experimental results, obtained from both simulated and real robot data, demonstrate the effectiveness of the approach....

We explore the advantages of representing hierarchical partially observable Markov decision processes (H-POMDPs) as dynamic Bayesian networks (DBNs). In particular, we focus on the special case of using H-POMDPs to represent multiresolution spatial maps for indoor robot navigation. Our results show that a DBN representation of H-POMDPs can train significantly faster than the original learning algorithm for H-POMDPs or the equivalent flat POMDP, and requires much less data. In addition, the DBN formulation can easily be extended to parameter tying and factoring of variables, which further reduces the time and sample complexity. This enables us to apply H-POMDP methods to much larger problems than previously possible. 1.