A new shape-based clustering algorithm for time series

• We propose to use fractional order correlation to measure the relationship between two sequences and apply the normalized form of the results to create the fractional order shape-based distance between two sequences. • We use the average sequence calculation method DBA to determine the cluster center and then combine it with our distance to cluster the time series. • We also combine our distance with the center determination strategy of other clustering algorithms to execute comparative experiments . • Experiments show that our method has improved the clustering accuracy. Our proposed distance can achieve better results when combined with a variety of strategies. At the same time, in the shape-based clustering algorithm, compared with the best KShape algorithm, we can also achieve better results. Time series clustering is a research hotspot in data mining. Most of the existing clustering algorithms combine with the classical distance measure which ignore the offset of sequence shape. As a result, shape-based clustering algorithms are becoming increasingly popular. On the majority of data sets, the most representative shape-based clustering algorithm, KShape, which defines a shape-based distance with shift invariance, has been shown to outperform other algorithms. In this paper, we propose a new shape-based clustering algorithm named Fractional Order Shape-based k-cluster(FrOKShape), which defines a multi-variable shape-based distance by normalized fractional order cross-correlation and uses the DTW Barycenter Averaging (DBA) as a center computation strategy. Our distance exhibits excellent shape shift deviating properties and good compatibility integrated with a variety of existing clustering center strategies so that it can provide more potential good results. Experiments show that combining our distance with a traditional clustering algorithm produces excellent clustering indicators. In a series of comparative experiments, FrOKShape also exhibits a comparable result to the existing better shape-based clustering algorithm KShape.