A hidden Markov model segmentation procedure for hydrological and environmental time series

Abstract

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Hubert's segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Hubert's least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.

A study on hydrological series of the Niger River

“…It allows one to determine whether a series is stationary or not, and divide it, should it not be stationary, into as many homogeneous series as possible. Based on the same principles, the segmentation procedure algorithm has been recently improved to deal with very long time series (Kehagias et al 2004, 2006, 2010, Gedikli et al 2008, 2010.…”

Using Markov Models to Mine Temporal and Spatial Data

“…Several methods have been proposed to perform such a segmentation. Markov chains Grant et al (1990) and HMM1 (Kehagias, 2004) are also been used.…”

An algorithm for optimal partitioning of data on an interval

“…An extensive discussion of precisely the same problem addressed here, but with a different approach to its solution, is in [3], [4]. Work by Hubert [10], [11], with applications to meteorology, influenced Kehagias and co-workers [8], [15], [16], [17], [18], [19], who developed a dynamic programming algorithm much like ours, for applications such as text segmentation (see also [9]), where the raw data are provided in the form of a similarity matrix. [22] gives an O(kN 2 ) dynamic programming algorithm for finding the optimal partition of an interval into k blocks, for a given k. See also [20], [2] for related work.…”