Tytuł | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
Publication Type | Journal Article |
Rok publikacji | 2019 |
Autorzy | Domino K, Gawron P |
Journal | International Journal of Applied Mathematics and Computer Science |
Volume | 29 |
Issue | 1 |
Start Page | 195 |
Date Published | 2019 |
Słowa kluczowe | data streaming, High order cumulants, non-normally distributed data, time-series statistics |
Abstract | High order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary order in a sliding window for data streams. To present an application of the algorithm, we propose a measure of non-normality of data stream based on tensor norms of high order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a~data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ the block structure to store and calculate only one hyper-pyramid part of such tensors. |
DOI | 10.2478/amcs-2019-0015 |