THE TENSOR DECOMPOSITION OF THE DATA MINING TECHNOLOGY: TIME SERIES ANALYSIS
DOI:
https://doi.org/10.18372/2310-5461.30.10562Keywords:
time row, tensor, matrix equation, anomalies, trand, trace, invariantsAbstract
In the article method of intellectual analysis TS, realised in the manner of deciding the matrix equations, link consequent tensor-windows TS, at a level rate of univariate models is considered. Incorpo-rated generalise feature of minimum fragment. Deciding the matrix equations allow calculate invariants (traces, norms and others), matrixes of singular values, Frobenius distances between matrixes, define trands of traces, norms, distances; change of trand a sign of anomaly TS or falling out of conditions a rate.
References
Cheboli D. Anomaly Detection of Time Series. Facility Of The Graduate School Of The Uni-versity Of Minnesota. — 2010. — 75 c. — [Электронный ресурс] — Режим доступа: http://con-servancy.umn. edu/bitstream /11299/92985/1/Cheboli_Deepthi_May2010.pdf (дата обращения:20. 04.2014).
Foslien W., Guralnik V., Haigh K. — Z. Data Mining For Space Applications. SpaceOps 2004 — Conference. Montreal, Canada — May 17–21 2004. Honeywell Laboratories, 3660 Techno-logy Drive, Minneapolis, MN 55418.
Binglin X., Zhanhuai L. An Anomaly Detection Method for Spacecraft Using ICA Technology. Inter-national Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013). — Р. 50–54
Mahoney Mat. V. and Chan Ph. K. Trajectory Boundary Modeling of Time Series for Anomaly Detection. KDD-05, Aug. 21, 2005, Chicago IL, USA. Copyright 2005 ACM 1-58113-000-0/00/ 0004.
Арский Ю. М. Принципы конструирования интеллектуальных систем / Ю. М. Арский, В. К. Финн // Информационные технологии и вычислительные системы. — № 4/2008. — С. 1–37.
Cichocki A. Tensor Decompositions: A New Concept in Brain Data Analysis arXiv: 1305. 0395v1 [cs.NA] 2 May 2013. — 19 рр.
Iverson D. L. System Health Monitoring for Space Mission Operations. Интернет-ресурс: http://ti.arc. nasa. gov/m/pub-archive/1389h/1389%20 (Iverson).pdf
Кендалл М. Дж. Курс статистики (в 3-х то-мах) / М.Дж. Кендалл, А. Стьюарт. — М. : Наука, Физматлит: 1966, 1973, 1976. — С.: 588+466+375. Т. 3. Многомерный статистический анализ и временные ряды.
Хеннан Э. Многомерные временные ряды / Э. Хеннан. — М. : Мир, 1974. — 576 с.
Главные компоненты временных рядов: метод «Гусеница»; под ред. Д. Л. Данилова, А. А. Жиглявского. СПб. : Пресском, 1997. —308 с.
Эсбенсен К. Анализ многомерных данных. Избранные главы / К. Эсбенсен; пер. с англ. С. В. Кучерявского; под ред. О. Е. Родионовой. — Черноголовка : ИПХФ РАН,2005. — 160 с.
Han J., Kamber M. Data Mining: Concepts and Techniques, 3rd ed. The Morgan Kaufmann Series in Data Management Systems, Jim Gray, Series Editor Morgan Kaufmann Publishers, March 2011.
Rogers M., Li L., Russell St. Multilinear Dynamical Systems for Tensor Time Series. In book “Advances in Neural Information Processing Systems” (NIPS 2013). — 2013. — P. 2634–2642.
Dobos L., Abonyiи J. Online detection of homogeneous operation ranges by dynamic principal component analysis based time-series segmentation // Chemical Engineering Science 75 (2012). — Р. 96–105.
Ringberg H., Soule A., Rexford J., Diot Ch. Sensitivity of PCA for Traffic Anomaly Detection // SIGMETRICS’07, June 12–16, 2007, San Diego, California, USA. Copyright 2007 ACM 978-1-59593-639-4/07/0006.
Skillicorn D. Data Mining and Knowledge Discovery Series. Understanding Complex Datasets. Data Mining with Matrix Decompositions. Chapman & Hall/CRC.- 2007.- 257 рр.
Laub A. J. Matrix Analysis for Scientists and Engineers. — 2005. — 158 р. Интернет-ресурс: www.csecurehost.com/SIAM/ot91.html
Kamalja K. K., Khangar N. V. Singular Value Decomposition for Multidimensional Matrices Int. Journal of Engineer. Research and Applications: 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013. — Р. 123–129.
Lototsky S. V. Simple spectral bounds for sums of certain Kronecker products. Linear Algebra and its Applications // 469 (2015). — Р. 114–129.
COM521500 Math. Methods for SP I Lecture 11: Matrix Equations and the Kronecker Product. Режим доступа : http://www.oz.-nthu.edu.tw/~d915691/files_com521 5/lecture 11(1222).pdf (дата обращения 14.04.2016).