Abstract
An appropriate definition and efficient computation of similarity (or distance) measures between two stochastic models are of theoretical and practical interest. In this work, a similarity measure, that is, a modified generalized probability product kernel, of Gaussian hidden Markov models is introduced. Two efficient schemes for computing this similarity measure are presented. The first scheme adopts a forward procedure analogous to the approach commonly used in probability evaluation of observation sequences on HMMs. The second scheme is based on the specially defined similarity transition matrix of two Gaussian hidden Markov models. Two scaling procedures are also proposed to solve the out-of-precision problem in the implementation. The effectiveness of the proposed methods has been evaluated on simulated observations with predefined model parameters, and on natural texture images. Promising experimental results have been observed.
Highlights
Hidden Markov model (HMM) has been adopted in a wide variety of application areas including econometrics, computational biology, statistical process control, and speech recognition
We first use simulated model parameters to test the effectiveness of the introduced similarity measure of Gaussian HMMs
We introduced a similarity measure of Gaussian HMMs based on a modified “generalized probability product kernel” definition
Summary
Hidden Markov model (HMM) has been adopted in a wide variety of application areas including econometrics, computational biology, statistical process control, and speech recognition. The modification is developed based on a new interpretation of GPPK Under this new interpretation, the similarity measure of two HMMs is considered as the statistical average of similarities of all possible so-called costate sequences drawn from the two HMMs. the brute-force computation of the similarity between two Gaussian HMMs can be prohibitively intensive, for example, the computational complexity is O(3T(NN )T+1), where T is the number of transitions and N and N are the numbers of states of two HMMs. In this work, we propose two fast schemes which can drastically ease this burden by reducing the computational complexity to O(3T(NN )2) and O((NN ) log T), respectively.
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