|Title||An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||Domino K, Gawron P|
|Journal||International Journal of Applied Mathematics and Computer Science|
|Keywords||data streaming, High order cumulants, non-normally distributed data, time-series statistics|
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.