A low complexity simulated annealing approach for training hidden Markov models

An algorithm for the training of Hidden Markov Models (HMMs) by simulated annealing is presented. This algorithm is based on a finite coding of the solution space based on the optimal trajectory of the state. It is applied to both discrete and continuous Gaussian observations. The algorithm needs no specific initialisation of the initial HMM by the user, the cooling schedule being general and applicable to any specific model. The parameters of the algorithm (initial and final temperatures) are derived automatically from theoretical considerations. The objective function evaluations of the algorithm are made independent of the problem size in order to minimise the computation time. A comparative study between the conventional Baum–Welch algorithm, Viterbi based algorithm and our simulated annealing algorithm shows that our algorithm gives better results and overcome the problem of HMM initialisation needed by the others.