Scale-varying dynamic time warping based on hesitant fuzzy sets for multivariate time series classification

Multivariate time series (MTS) data widely exists in daily life. How to classify MTS remains a major problem in data mining, computer science, financial area and other relative industry. MTS data is always treated as a whole object or time instance one by one, while in this paper, time instance segments were paid more attention. A new distance measure named dynamic time warping based on hesitant fuzzy sets (HFS-DTW) is proposed for MTS classification. HFS-DTW is a generalized dynamic time warping algorithm, and due to the characteristic of HFS, it is easy to find optimal alignment between time instance segments. Also, the proposed method could be reduced to original DTW by setting scale parameters. In order to apply the proposed algorithm correctly and efficiently, the parameter constraints were discussed. Furthermore, using 10-fold cross-validation, five MTS data sets selected from the University of California, Irvine machine learning repository, were tested by the proposed algorithm. By comparing with state-of-the-art algorithms, the results demonstrate the proposed method could balance the higher accuracy and lower time-consuming in classification.