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

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-o...

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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
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Abstract	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.
AbstractList	This article aims to design a trend-oriented-granulation-based fuzzy [Formula Omitted]-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, [Formula Omitted] 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. This article aims to design a trend-oriented-granulation-based fuzzy C -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, l1 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.This article aims to design a trend-oriented-granulation-based fuzzy C -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, l1 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. 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.
Author	Jiang, Shurong Pedrycz, Witold Yang, Huilin Hao, Yadong Yu, Fusheng Yang, Zonglin
Author_xml	– sequence: 1 givenname: Zonglin surname: Yang fullname: Yang, Zonglin email: zonglinyang@mail.bnu.edu.cn organization: School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, China – sequence: 2 givenname: Shurong surname: Jiang fullname: Jiang, Shurong email: sxjiangsr@126.com organization: School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, China – sequence: 3 givenname: Fusheng orcidid: 0000-0001-9144-9150 surname: Yu fullname: Yu, Fusheng email: yufusheng@bnu.edu.cn organization: School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, China – sequence: 4 givenname: Witold orcidid: 0000-0002-9335-9930 surname: Pedrycz fullname: Pedrycz, Witold email: wpedrycz@ualberta.ca organization: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada – sequence: 5 givenname: Huilin surname: Yang fullname: Yang, Huilin email: huilinyang@mail.bnu.edu.cn organization: School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, China – sequence: 6 givenname: Yadong surname: Hao fullname: Hao, Yadong email: haoyadong132@foxmail.com organization: School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, China
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SubjectTerms	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
Title	Linear Fuzzy Information-Granule-Based Fuzzy C-Means Algorithm for Clustering Time Series
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