Sliding window high order cumulant tensors calculation algorithm

TitleSliding window high order cumulant tensors calculation algorithm
Publication TypeJournal Article
Year of Publication2017
AuthorsDomino K, Gawron P
JournalarXiv:
Volume1701.06446
Date Published01/2017
Keywordsdata 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.

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