Implementation of hidden semi-Markov models

IEEE Signal Processing Magazine, 1986

The basic theory of Markov chains has been known to mathematicians and engineers for close to 80 years, but it is only in the past decade that it has been applied explicitly to problems in speech processing. One of the major reasons why speech models, based on Markov chains, have not been developed until recently was the lack of a method for optimizing the parameters of the Markov model to match observed signal patterns. Such a method was proposed in the late 1960's and was immediately applied to speech processing in several research institutions. Continued refinements in the theory and implementation of Markov modelling techniques have greatly enhanced the method, leading to a wide range of applications of these models. It is the purpose of this tutorial paper to give an introduction to the theory of Markov models, and to illustrate how they have been applied to problems in speech recognition.

Annals of Mathematics and Artificial Intelligence, 2017

Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure of data of interest, such as inputoutput relations and correlation among datasets. However, because most studies in this area are specialized or limited to their respective applications, rigorous requirement analysis of such models has not been undertaken from a general perspective. Therefore, we particularly examine the structure of sequential data, and extract the necessity of "state duration" and "state interval" of events for efficient and rich representation of sequential data. Specifically addressing the hidden semi-Markov model (HSMM) that represents such state duration inside a model, we attempt to add representational capability of a state interval of events onto HSMM. To this end, we propose two extended models: an interval state hidden semi-Markov model (IS-HSMM) to express the length of a state interval with a special state node designated as "interval state node"; and an interval length probability hidden semi-Markov model (ILP-HSMM) which represents the length of the state interval with a new probabilistic parameter "interval length probability." Exhaustive simulations have revealed superior performance of the proposed models in comparison with HSMM. These proposed models are the first reported extensions of HMM to support state interval representation as well as state duration representation.

2002

Bourlard & Bengio: Hidden Markov Models and other Finite State Automata 2 During these last 20 years, Finite State Automata (FSA), and more particularly Stochastic Finite State Automata (SFSA) and different variants of Hidden Markov Models (HMMs), have been used quite successfully

A Classification problem can be viewed as a problem of assigning a category or class to a given input. The Hidden Markov model is a well known stochastic model that is used to solve classification problems and has been widely exploited in diverse computing applications ranging from speech, acoustics, gesture recognition to part-of-speech tagging, cryptography to Google page rank and the list goes on. State Complexity of Deterministic Finite automata is now a well established research area. State complexity of Deterministic Finite Automata defines the total number of states in the minimal Deterministic Finite Automata. State complexity, if known, of a given automata helps to realize how expensive the application would be that will exploit that automata. Similarly, if known, the state complexity of the Hidden Markov Model will help to know the complexity of a computing application that exploits that Hidden Markov Model. In this paper, we have explored several, yet unpublished, important facts about the Hidden Markov Model including the state complexity of Hidden Markov Model and the diagram of 2nd order Hidden Markov Model . Our discussion of the Hidden Markov Model is unique in the sense that we present a complete diagram of the 1 st order Hidden Markov Model with all estimated parameters for a given input sequence. We explicitly define a generalized rule to give "Dimension of Transition probability matrix of HMM" which is also not available in the literature yet. We present a generalized rule to draw the M th order Hidden Markov Model diagram for M greater than 1. We present the generalized state complexity of the M th Order HMM, the state complexity of the diagram for the "Training of M th Order HMM" and also present the diagram for second order Hidden Markov Model.

2000

1999

The Department of Information Science is one of six departments that make up the Division of Commerce at the University of Otago. The department offers courses of study leading to a major in Information Science within the BCom, BA and BSc degrees. In addition to undergraduate teaching, the department is also strongly involved in postgraduate research programmes leading to MCom, MA, MSc and PhD degrees. Research projects in spatial information processing, connectionist-based information systems, software engineering and software development, information engineering and database, software metrics, distributed information systems, multimedia information systems and information systems security are particularly well supported.

This paper performs a state-of-the-art literature review to classify and interpret the ongoing and emerging issues associated with the Hidden Markov Model (HMM) in the last decade. HMM is a commonly used method in many scientific areas. It is a temporal probabilistic model in which the state of the process is described by a single discrete ran-dom variable. The theory of HMMs was developed in the late 1960s. Now, it is especially known for its application in temporal pattern recognition, i.e. speech, handwriting, and bioinformatics. After a brief description of the study methodology, this paper comprehensively compares the most impor-tant HMM publications by field of interest, most cited authors, authors' nationalities, and scientific journals. The comparison is based on papers in-dexed in the Institute for Scientific Information (ISI) Web of Knowledge and ScienceDirect data-bases.

Proceedings of ICICS