Diagonalization Matrix Method of Solving the First Problem of Hidden Markov Model in Speech Recognition System

TL;DR

This paper introduces a diagonalization matrix method to efficiently evaluate the observation probability in Hidden Markov Models for speech recognition, reducing computational effort compared to traditional methods.

Contribution

It presents a novel diagonalization approach for computing matrix powers, improving efficiency in solving the HMM evaluation problem.

Findings

Diagonalization method reduces computational time.

Compared to direct methods, the new approach is more efficient.

Method is suitable for large-scale HMM evaluation.

Abstract

This paper proposes a computationally efficient method of solving evaluation problem of Hidden Markov Model (HMM) with a given set of discrete observation symbols, number of states and probability distribution matrices. The observation probability for a given HMM model is evaluated using an approach in which the probability evaluation is reduced to the problem of evaluating the product of matrices with different powers and formed out of state transition probabilities and observation probabilities. Finding powers of a matrix is done by using the computationally efficient diagonalization method thereby reducing the overall computational effort for evaluating the Evaluation problem of HMM.The proposed method is compared with the existing direct method. It is found that evaluating matrix power by diagnolisation method is more suitable than that of the direct, method.