State reduction in hidden Markov chains used for speech recognition

This paper examines the problem of reducing the number of states in the Markov chain models used in speech recognition algorithms by statistical methods. It is shown that the equivalence requirements between the original and reduced model lead to entirely different reduction equations depending on whether the reduction occurs inside a word model or between the models of different words. In general, the exact solution of these reduction equations is not possible and one shows that a least-squares solution can be reformulated as a matrix approximation problem in Euclidean norm.