A granulation-based method for finding similarity between time series

In this paper, a granulation-based method for finding similarity between two time series is proposed. Firstly, for each time series X = {x₁, x₂,..., x_n}, the approach develops a granular time series induced by the original time series, and a trend granular time series induced by the trend time series ∂X = {x₂ - x₁, x₃ - x₂,..., x_n - x_n-1}. Secondly, it compares the two original time series by comparing the corresponding two (trend) granular time series. In order to compare two (trend) granular time series, an index, named degree of similarity, is defined to reflect the similarity of them. By the granulation-based method, we can deal with the temporal data mining tasks such as similar subsequence searching, clustering and indexing etc. on the granular level. Experiments show that our method is effective and applicable.