Linear Fuzzy Information-Granule-Based Fuzzy C-Means Algorithm for Clustering Time Series

• Published in: IEEE transactions on cybernetics Vol. 53; no. 12; pp. 7622 - 7634
• Main Authors: Yang, Zonglin, Jiang, Shurong, Yu, Fusheng, Pedrycz, Witold, Yang, Huilin, Hao, Yadong
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clustering; Clustering algorithms; Dynamic time warping (DTW); fuzzy C-means (FCM); Granular materials; Granulation; Heuristic algorithms; Iterative methods; linear fuzzy information granule (LFIG); l₁ trend filtering; Merging; Prototypes; Segments; Time measurement; Time series; Time series analysis; time-series clustering; Trends
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2022.3184999

This article aims to design a trend-oriented-granulation-based fuzzy <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula>-means (FCM) algorithm that can cluster a group of time series at an abstract (granular) level. To achieve a better trend-oriented granulation of a time series, <inline-formula> <tex-math notation="LaTeX">{l}_{1} </tex-math></inline-formula> trend filtering is firstly carried out to result in segments which are then optimized by the proposed segment merging algorithm. By constructing a linear fuzzy information granule (LFIG) on each segment, a granular time series which well reflects the linear trend characteristic of the original time series is produced. With the novel designed distance that can well measure the trend similarity of two LFIGs, the distance between two granular time series is calculated by the modified dynamic time warping (DTW) algorithm. Based on this distance, the LFIG-based FCM algorithm is developed for clustering time series. In this algorithm, cluster prototypes are iteratively updated by the specifically designed granule splitting and merging algorithm, which allows the lengths of prototypes to change in the process of iteration. This overcomes the serious drawback of the existing approaches, where the lengths of prototypes cannot be changed. Experimental studies demonstrate the superior performance of the proposed algorithm in clustering time series with different shapes or trends.