<abstract xmlns="http://www.w3.org/1999/xhtml"><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 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.</p></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.

An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

High-order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm...

An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams

Published Online: Mar 29, 2019

Page range: 195 - 206

Received: Apr 05, 2018

Accepted: Oct 03, 2018

DOI: https://doi.org/10.2478/amcs-2019-0015

Keywords
high order cumulants, time-series statistics, non-normally distributed data, data streaming

© 2019 Krzysztof Domino et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams

Published Online: Mar 29, 2019

Page range: 195 - 206

Received: Apr 05, 2018

Accepted: Oct 03, 2018

DOI: https://doi.org/10.2478/amcs-2019-0015

Keywordshigh order cumulants, time-series statistics, non-normally distributed data, data streaming

© 2019 Krzysztof Domino et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
high order cumulants, time-series statistics, non-normally distributed data, data streaming