Abstract
Information granules can discover interpretable and meaningful relationships offering a full description for time series. This article presents an information granulation method with rectangular information granules and applies it to time-series similarity measurement. First, the fuzzy $c$-means clustering algorithm transforms the time series and its first-order difference time series to data clusters. With the maximum volume of rectangular information granules viewed as the criterion, the optimal rectangular information granules are formed using the data cluster by the principle of justifiable granularity and the gravitational search algorithm. The time-series similarity is measured by calculating the similarity between the upper and lower bounds of the optimal rectangular information granules built from the time series. Finally, an experiment is performed on a public dataset to verify the feasibility of the proposed method. The result shows that the rectangular information granulation method can capture the change characteristics of time series. The similarity measurement method can effectively evaluate the similarity of the time series belonging to different classes.