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Paper details
Number 1 - March 2019
Volume 29 - 2019
An algorithm for arbitrary-order cumulant tensor calculation in a sliding window of data streams
Krzysztof Domino, Piotr Gawron
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 orders in a sliding window for data streams.
We show that this algorithm offers substantial speedups of cumulant updates compared with the current solutions. The
proposed algorithm can be used for processing on-line high-frequency multivariate data and can find applications, e.g.,
in on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an
estimator of non-Gaussianity of a data stream based on the 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 a block structure to store and
calculate only one hyper-pyramid part of such tensors.
Keywords
high order cumulants, time-series statistics, non-normally distributed data, data streaming