01088nas a2200145   4500000000100000000000100001008004100002260000900043100002100052700001700073245010300090300000800193490000700201520073400208       2019                            d  c20191 aKrzysztof Domino1 aPiotr Gawron00aAn algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams  a2060 v293 a<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>