Domino, Krzysztof ; Gawron, Piotr
Contributor:Gamper, Johann - ed. ; Wrembel, Robert - ed.
Title:An algorithm for arbitrary-order cumulant tensor calculation in a sliding window of data streams
Subtitle: Group publication title: Subject and Keywords:high order cumulants ; time-series statistics ; non-normally distributed data ; data streaming
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.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 29, number 1 (2019) ; click here to follow the link
Language: License CC BY 4.0: Rights: