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>