Abstract
In this paper, time-series clustering is discussed. At first ℓ1 trend filtering method is used to produce an optimal segmentation of time series. Next optimized fuzzy information granulation is completed for each segment to form a linear fuzzy information granule, which includes both average and trend information. Once the optimal segmentation and granulation have been completed, the original time series is transformed into a granular time series. To finalize time-series clustering, a distance measure for granular time series is established, and a linear fuzzy information granule-based dynamic time warping (LFIG_DTW) algorithm is developed for calculating the distance of two equal-length or unequal-length granular time series. Furthermore, the distance realized by the LFIG_DTW algorithm can detect not only the increasing or decreasing trends, but also the changing periods and rates of changes. After calculating all the distances between any two granular time series, a LFIG_DTW distance-based hierarchical clustering method is designed for time-series clustering. Experiment results involving several real datasets show the effectiveness of the proposed method.
•Propose an optimal method for time series granulation based on ℓ1 trend filtering and LFIG.•Give a new distance of LFIGs that generalizes the version of equal-size case.•Propose a distance measure method for granular time series composed of unequal-size LFIGs.•Propose a clustering method based on the proposed distance measure.