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It begins with an insight that subsequences in a periodic time series can be treated as sets of independent and identically distributed (iid) points generated from an unknown distribution in R. This R domain treatment enables two new possibilities: (a) the similarity between two subsequences can be computed using a distributional measure such as Wasserstein distance (WD), kernel mean embedding or Isolation Distributional kernel (IDK); and (b) these distributional measures become non-sliding-window-based. Together, they offer an alternative that has more effective similarity measurements and runs significantly faster than the point-to-point and sliding-window-based measures. Our empirical evaluation shows that IDK and WD are effective distributional measures for time series; and IDK-based detectors have better detection accuracy than existing sliding-window-based detectors, and they run faster with linear time complexity.<\/jats:p>","DOI":"10.14778\/3551793.3551796","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T22:25:03Z","timestamp":1664490303000},"page":"2321-2333","source":"Crossref","is-referenced-by-count":16,"title":["A new distributional treatment for time series and an anomaly detection investigation"],"prefix":"10.14778","volume":"15","author":[{"given":"Kai Ming","family":"Ting","sequence":"first","affiliation":[{"name":"Nanjing University, China"}]},{"given":"Zongyou","family":"Liu","sequence":"additional","affiliation":[{"name":"Nanjing University, China"}]},{"given":"Hang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Nanjing University, China"}]},{"given":"Ye","family":"Zhu","sequence":"additional","affiliation":[{"name":"Deakin University, Australia"}]}],"member":"320","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Unsupervised and scalable subsequence anomaly detection in large data series. 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In Proceedings of the 6th International Congress on Acoustics. 280--292."},{"key":"e_1_2_1_12_1","volume-title":"Exemplar learning for extremely efficient anomaly detection in real-valued time series. Data mining and knowledge discovery 30, 6","author":"Jones Michael","year":"2016","unstructured":"Michael Jones , Daniel Nikovski , Makoto Imamura , and Takahisa Hirata . 2016. Exemplar learning for extremely efficient anomaly detection in real-valued time series. Data mining and knowledge discovery 30, 6 ( 2016 ), 1427--1454. Michael Jones, Daniel Nikovski, Makoto Imamura, and Takahisa Hirata. 2016. Exemplar learning for extremely efficient anomaly detection in real-valued time series. Data mining and knowledge discovery 30, 6 (2016), 1427--1454."},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of the IEEE International Conference on Data Mining. 226--233","author":"Keogh E.","unstructured":"E. Keogh , J. Lin , and A. Fu . 2005. HOT SAX: efficiently finding the most unusual time series subsequence . In Proceedings of the IEEE International Conference on Data Mining. 226--233 . E. Keogh, J. Lin, and A. Fu. 2005. HOT SAX: efficiently finding the most unusual time series subsequence. In Proceedings of the IEEE International Conference on Data Mining. 226--233."},{"key":"e_1_2_1_14_1","volume-title":"Exact indexing of dynamic time warping. Knowledge and Information Systems 7 (01","author":"Keogh Eamonn","year":"2005","unstructured":"Eamonn Keogh and Chotirat Ratanamahatana . 2005. Exact indexing of dynamic time warping. Knowledge and Information Systems 7 (01 2005 ), 358--386. Eamonn Keogh and Chotirat Ratanamahatana. 2005. Exact indexing of dynamic time warping. Knowledge and Information Systems 7 (01 2005), 358--386."},{"key":"e_1_2_1_15_1","volume-title":"Statistical Visions in Time: A History of Time Series Analysis, 1662--1938","author":"Klein Judy L.","unstructured":"Judy L. Klein . 2005. 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In Proceedings of the 24th International Conference on Very Large Data Bases. 392--403."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2008.17"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/51.932724"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1561\/9781680832891"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.5555\/3023638.3023684"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2949741.2949758"},{"key":"e_1_2_1_22_1","volume-title":"Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data. 1887--1905","author":"Paparrizos John","unstructured":"John Paparrizos , Chunwei Liu , Aaron J. Elmore , and Michael J. Franklin . 2020. Debunking Four Long-Standing Misconceptions of Time-Series Distance Measures . In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data. 1887--1905 . John Paparrizos, Chunwei Liu, Aaron J. Elmore, and Michael J. Franklin. 2020. Debunking Four Long-Standing Misconceptions of Time-Series Distance Measures. In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data. 1887--1905."},{"key":"e_1_2_1_23_1","volume-title":"Fundamentals of Probability and Stochastic Processes with Applications to Communications","author":"Park Kun Il","unstructured":"Kun Il Park . 2018. Fundamentals of Probability and Stochastic Processes with Applications to Communications . Springer Publishing Company, Inc orporated. Kun Il Park. 2018. Fundamentals of Probability and Stochastic Processes with Applications to Communications. Springer Publishing Company, Incorporated."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33014755"},{"key":"e_1_2_1_25_1","volume-title":"Encyclopedia of Mathematics","author":"Rueshendorff L.","unstructured":"L. Rueshendorff . 2002. Wasserstein metric . In Encyclopedia of Mathematics . EMS Press . L. 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In Proceedings of the 7th International Congress on Acoustics. 65--69."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1978.1163055"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1162\/089976601750264965"},{"key":"e_1_2_1_29_1","volume-title":"Proceedings of the 18th International Conference on Extending Database Technology. 481--492","author":"Senin Pavel","year":"2015","unstructured":"Pavel Senin , Jessica Lin , Xing Wang , Tim Oates , Sunil Gandhi , Arnold P Boedihardjo , Crystal Chen , and Susan Frankenstein . 2015 . Time series anomaly discovery with grammar-based compression . In Proceedings of the 18th International Conference on Extending Database Technology. 481--492 . Pavel Senin, Jessica Lin, Xing Wang, Tim Oates, Sunil Gandhi, Arnold P Boedihardjo, Crystal Chen, and Susan Frankenstein. 2015. Time series anomaly discovery with grammar-based compression. In Proceedings of the 18th International Conference on Extending Database Technology. 481--492."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975321.27"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3261-0"},{"key":"e_1_2_1_32_1","volume-title":"A Hilbert Space Embedding for Distributions","author":"Smola Alex","unstructured":"Alex Smola , Arthur Gretton , Le Song , and Bernhard Sch\u00f6lkopf . 2007. A Hilbert Space Embedding for Distributions . In Algorithmic Learning Theory, Marcus Hutter, Rocco A. Servedio, and Eiji Takimoto (Eds.). Springer , 13--31. Alex Smola, Arthur Gretton, Le Song, and Bernhard Sch\u00f6lkopf. 2007. A Hilbert Space Embedding for Distributions. In Algorithmic Learning Theory, Marcus Hutter, Rocco A. Servedio, and Eiji Takimoto (Eds.). Springer, 13--31."},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975673.59"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-021-00785-1"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/3394486.3403062"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2021.3120277"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/3219819.3219990"},{"key":"e_1_2_1_38_1","unstructured":"Matteo Togninalli Elisabetta Ghisu Felipe Llinares-L\u00f3pez Bastian Rieck and Karsten Borgwardt. 2019. Wasserstein Weisfeiler-Lehman Graph Kernels. In Advances in neural information processing systems.  Matteo Togninalli Elisabetta Ghisu Felipe Llinares-L\u00f3pez Bastian Rieck and Karsten Borgwardt. 2019. Wasserstein Weisfeiler-Lehman Graph Kernels. 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