Time series data are often clustered repeatedly across various time ranges to mine frequent subsequence patterns from different periods, which could further support downstream applications. Existing state-of-the-art (SOTA) time series clustering method, such as K-Shape, can proficiently cluster time series data referring to their shapes. However, in-database time series clustering problem has been neglected, especially in IoT scenarios with large-volume data and high efficiency demands. Most time series databases employ LSM-Tree based storage to support intensive writings, yet causing underlying data points out-of-order in timestamps. Therefore, to apply existing out-of-database methods, all data points must be fully loaded into memory and chronologically sorted. Additionally, out-of-database methods must cluster from scratch each time, making them inefficient when handling queries across different time ranges. In this work, we propose an in-database adaptation of SOTA time series clustering method K-Shape. Moreover, to solve the problem that K-Shape cannot efficiently handle long time series, we propose Medoid-Shape, as well as its in-database adaptation for further acceleration. Extensive experiments are conducted to demonstrate the higher efficiency of our proposals, with comparable effectiveness. Remarkably, all proposals have already been implemented in an open-source commodity time series database, Apache IoTDB.

Dirty data commonly exist. Simply discarding a large number of inaccurate points (as noises) could greatly affect clustering results. We argue that dirty data can be repaired and utilized as strong supports in clustering. To this end, we study a novel problem of clustering and repairing over dirty data at the same time. Referring to the minimum change principle in data repairing, the objective is to find a minimum modification of inaccurate points such that the large amount of dirty data can enhance clustering. We show that the problem isNP-hard and can be formulated as an integer linear programming (ILP) problem. A constant factor approximation algorithmGDORCis devised based on grid, with high efficiency. In experiments,GDORChas great repairing and clustering results with low time consumption. Empirical results demonstrate thatboth the clustering and cleaning accuraciescan be improved by our approach of repairing and utilizing the dirty data in clustering.