An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams
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 speedu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2019-03-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amcs-2019-0015 |
| _version_ | 1818735818388275200 |
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| author | Domino Krzysztof Gawron Piotr |
| author_facet | Domino Krzysztof Gawron Piotr |
| author_sort | Domino Krzysztof |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T00:27:18Z |
| format | Article |
| id | doaj.art-81fc70efbc5a40448b3bf522ceca68fb |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-18T00:27:18Z |
| publishDate | 2019-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-81fc70efbc5a40448b3bf522ceca68fb2022-12-21T21:27:13ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922019-03-0129119520610.2478/amcs-2019-0015amcs-2019-0015An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streamsDomino Krzysztof0Gawron Piotr1Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100Gliwice, PolandInstitute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100Gliwice, PolandHigh-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.https://doi.org/10.2478/amcs-2019-0015high order cumulantstime-series statisticsnon-normally distributed datadata streaming |
| spellingShingle | Domino Krzysztof Gawron Piotr An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams International Journal of Applied Mathematics and Computer Science high order cumulants time-series statistics non-normally distributed data data streaming |
| title | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| title_full | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| title_fullStr | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| title_full_unstemmed | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| title_short | An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams |
| title_sort | algorithm for arbitrary order cumulant tensor calculation in a sliding window of data streams |
| topic | high order cumulants time-series statistics non-normally distributed data data streaming |
| url | https://doi.org/10.2478/amcs-2019-0015 |
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