A Fast Two-Stage Dynamic Programming Algorithm for Change-Points Model with Application in Speech Signal

In multiple change-points model, the dynamic programming (DP) algorithm can be use to obtain the maximum likelihood estimation for a sequence of data from multivariate normal distribution. Since the algorithm has a quadratic complexity in data size n, it is computationally burdensome if the data size n is large. In this paper we present a fast two-stage dynamic programming (TSDP) through the window method. In TSDP algorithm, the first stage is to use the window method based on the log-likelihood ratio measure to find a subset of candidate change points. The second stage is to apply DP algorithm on the chosen subset to detect the position of change points. The proposed algorithm of change-points will be used for the boundary detection of speech signal by finding the abrupt spectral difference change of adjacent frames. Some simulated data sets and the speech data are investigated for DP and TSDP algorithms. In comparison of CPU times, the TSDP algorithm can be up to 34.96 and 74.02 times faster than the DP algorithm for the simulated data and the speech data respectively. The results show that our algorithm works very well. It substantially reduces the computation load for large data size n.