Time-series clustering based on linear fuzzy information granules

Abstract In this paper, time-series clustering is discussed. At first l 1 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.

[1]  Raja Jayaraman,et al.  Support vector-based algorithms with weighted dynamic time warping kernel function for time series classification , 2015, Knowl. Based Syst..

[2]  Mirjana Ivanovic,et al.  The Influence of Global Constraints on Similarity Measures for Time-Series Databases , 2011, Knowl. Based Syst..

[3]  Li Wei,et al.  Compression-based data mining of sequential data , 2007, Data Mining and Knowledge Discovery.

[4]  Xiaohu Yang,et al.  Radian-distance Based Time Series Similarity Measurement: Radian-distance Based Time Series Similarity Measurement , 2011 .

[5]  Hongqing Zhu,et al.  Merging Student's-t and Rayleigh distributions regression mixture model for clustering time-series , 2017, Neurocomputing.

[6]  Olgierd Hryniewicz,et al.  Bayesian analysis of time series using granular computing approach , 2016, Appl. Soft Comput..

[7]  Chellu Chandra Sekhar,et al.  Large margin mixture of AR models for time series classification , 2013, Appl. Soft Comput..

[8]  Stephen P. Boyd,et al.  1 Trend Filtering , 2009, SIAM Rev..

[9]  Vit Niennattrakul,et al.  Selective Subsequence Time Series clustering , 2012, Knowl. Based Syst..

[10]  Maciej Krawczak,et al.  An approach to dimensionality reduction in time series , 2014, Inf. Sci..

[11]  Zheng Zhang,et al.  Dynamic Time Warping under limited warping path length , 2017, Inf. Sci..

[12]  Hongxun Yao,et al.  Strategy for dynamic 3D depth data matching towards robust action retrieval , 2015, Neurocomputing.

[13]  Weihua Xu,et al.  A novel cognitive system model and approach to transformation of information granules , 2014, Int. J. Approx. Reason..

[14]  Witold Pedrycz,et al.  Temporal granulation and its application to signal analysis , 2002, Inf. Sci..

[15]  Witold Pedrycz,et al.  The modeling of time series based on fuzzy information granules , 2014, Expert Syst. Appl..

[16]  Witold Pedrycz,et al.  Granular Data Description: Designing Ellipsoidal Information Granules , 2017, IEEE Transactions on Cybernetics.

[17]  Jian-ye Zhang,et al.  Similarity Search Method in Time Series Based on Curvature Distance: Similarity Search Method in Time Series Based on Curvature Distance , 2013 .

[18]  Alessandro Giusti,et al.  Robust classification of multivariate time series by imprecise hidden Markov models , 2015, Int. J. Approx. Reason..

[19]  Elizabeth Ann Maharaj,et al.  Fuzzy clustering of time series in the frequency domain , 2011, Inf. Sci..

[20]  Witold Pedrycz,et al.  Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system , 2017, Int. J. Approx. Reason..

[21]  Ying Wah Teh,et al.  Time-series clustering - A decade review , 2015, Inf. Syst..

[22]  Alireza Rahai,et al.  A fast and efficient clustering based fuzzy time series algorithm (FEFTS) for regression and classification , 2017, Appl. Soft Comput..

[23]  Dit-Yan Yeung,et al.  Time series clustering with ARMA mixtures , 2004, Pattern Recognit..

[24]  M. Ivanović,et al.  The Influence of Global Constraints on DTW and LCS Similarity Measures for Time-Series Databases , 2011 .

[25]  Jianling Sun,et al.  Piecewise statistic approximation based similarity measure for time series , 2015, Knowl. Based Syst..

[26]  Björn W. Schuller,et al.  A multidimensional dynamic time warping algorithm for efficient multimodal fusion of asynchronous data streams , 2009, Neurocomputing.

[27]  Bernhard Sick,et al.  Temporal data mining using shape space representations of time series , 2010, Neurocomputing.

[28]  Fabian Mörchen,et al.  Extracting interpretable muscle activation patterns with time series knowledge mining , 2005, Int. J. Knowl. Based Intell. Eng. Syst..

[29]  Witold Pedrycz,et al.  Fuzzy classifiers with information granules in feature space and logic-based computing , 2018, Pattern Recognit..

[30]  Witold Pedrycz,et al.  Using interval information granules to improve forecasting in fuzzy time series , 2015, Int. J. Approx. Reason..

[31]  Yasuo Kudo,et al.  A sequential pattern mining algorithm using rough set theory , 2011, Int. J. Approx. Reason..

[32]  Nor Ashidi Mat Isa,et al.  Knowledge base to fuzzy information granule: A review from the interpretability-accuracy perspective , 2017, Appl. Soft Comput..

[33]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[34]  Eamonn J. Keogh,et al.  A symbolic representation of time series, with implications for streaming algorithms , 2003, DMKD '03.

[35]  José G. Dias,et al.  Clustering financial time series: New insights from an extended hidden Markov model , 2015, Eur. J. Oper. Res..

[36]  Donald J. Berndt,et al.  Using Dynamic Time Warping to Find Patterns in Time Series , 1994, KDD Workshop.