Markov model based time series similarity measuring

Similarity or distance measures between two time series play an important role in analysis and retrieval of time series database, which is a fundamental problem in time series data mining. Mathematical model is widely used as a representation of time series, but few papers discuss it in similarity measure of time series. In this paper, we propose a Markov model based technique for similarity/distance measures of variable-length time sequences. State space of Markov model is partitioned by hierarchical clustering method, and the information of state-transition is used to represent a time series. The similarity/distance measures of time sequences can be defined as various functions of the difference between their state-transition information, and some widely used distance measures can be considered as our specific cases. In addition, in modeling procedure, the vector sequence in reconstructed phase space is used instead of the original time sequence, which more effectively reflects the dynamical property of time series. Experimental results show that it works well under the strong noise environment, and it is versatile for various applications by its flexible definition.