An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams
| Author | Domino K.; Gawron P. |
|---|---|
| Title | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| Journal | International Journal of Applied Mathematics and Computer Science |
| Year | 2019 |
| Status | Published |
| Volume | 29 |
| Issue | 1 |
| Pages | 206 |
| DOI | 10.2478/amcs-2019-0015 |
| Abstract | <p>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.</p> |