Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories
Abstract We propose a novel class of mixed fluctuations with different orientations and fractal scaling features as a model for anisotropic two-dimensional (2D) trajectories hypothesized to appear in complex systems. Furthermore, we develop the oriented fractal scaling component analysis (OFSCA) to...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2020-12-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-020-78807-z |
| _version_ | 1818421255345274880 |
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| author | Ivan Seleznov Anton Popov Kazuhei Kikuchi Elena Kolosova Bohdan Kolomiiets Akio Nakata Miki Kaneko Ken Kiyono |
| author_facet | Ivan Seleznov Anton Popov Kazuhei Kikuchi Elena Kolosova Bohdan Kolomiiets Akio Nakata Miki Kaneko Ken Kiyono |
| author_sort | Ivan Seleznov |
| collection | DOAJ |
| description | Abstract We propose a novel class of mixed fluctuations with different orientations and fractal scaling features as a model for anisotropic two-dimensional (2D) trajectories hypothesized to appear in complex systems. Furthermore, we develop the oriented fractal scaling component analysis (OFSCA) to decompose such mixed fluctuations into the original orientation components. In the OFSCA, the original orientations are detected based on the principle that the original angles are orthogonal to the angles with the minimum and maximum scaling exponents of the mixed fluctuations. In our approach, the angle-dependent scaling properties are estimated using the Savitzky–Golay-filter-based detrended moving-average analysis (DMA), which has a higher detrending order than the conventional moving-average-filter-based DMA. To illustrate the OFSCA, we demonstrate that the numerically generated time-series of mixed fractional Gaussian noise (fGn) processes with non-orthogonal orientations and different scaling exponents is successfully decomposed into the original fGn components. We demonstrate the existence of oriented components in the 2D trajectories by applying OFSCA to real-world time-series, such as human postural fluctuations during standing and seismic ground acceleration during the great 2011 Tohoku-oki earthquake. |
| first_indexed | 2024-12-14T13:07:27Z |
| format | Article |
| id | doaj.art-f939fff861984d3fa8c6f142c27effec |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-14T13:07:27Z |
| publishDate | 2020-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-f939fff861984d3fa8c6f142c27effec2022-12-21T23:00:17ZengNature PortfolioScientific Reports2045-23222020-12-0110111110.1038/s41598-020-78807-zDetection of oriented fractal scaling components in anisotropic two-dimensional trajectoriesIvan Seleznov0Anton Popov1Kazuhei Kikuchi2Elena Kolosova3Bohdan Kolomiiets4Akio Nakata5Miki Kaneko6Ken Kiyono7Graduate School of Engineering Science, Osaka UniversityDepartment of Electronic Engineering, Igor Sikorsky Kyiv Polytechnic InstituteSchool of Statistical Thinking, Institute of Statistical MathematicsScientific Research Institute, National University of Physical Education and Sport of UkraineDepartment of Electronic Engineering, Igor Sikorsky Kyiv Polytechnic InstituteGraduate School of Engineering Science, Osaka UniversityGraduate School of Engineering Science, Osaka UniversityGraduate School of Engineering Science, Osaka UniversityAbstract We propose a novel class of mixed fluctuations with different orientations and fractal scaling features as a model for anisotropic two-dimensional (2D) trajectories hypothesized to appear in complex systems. Furthermore, we develop the oriented fractal scaling component analysis (OFSCA) to decompose such mixed fluctuations into the original orientation components. In the OFSCA, the original orientations are detected based on the principle that the original angles are orthogonal to the angles with the minimum and maximum scaling exponents of the mixed fluctuations. In our approach, the angle-dependent scaling properties are estimated using the Savitzky–Golay-filter-based detrended moving-average analysis (DMA), which has a higher detrending order than the conventional moving-average-filter-based DMA. To illustrate the OFSCA, we demonstrate that the numerically generated time-series of mixed fractional Gaussian noise (fGn) processes with non-orthogonal orientations and different scaling exponents is successfully decomposed into the original fGn components. We demonstrate the existence of oriented components in the 2D trajectories by applying OFSCA to real-world time-series, such as human postural fluctuations during standing and seismic ground acceleration during the great 2011 Tohoku-oki earthquake.https://doi.org/10.1038/s41598-020-78807-z |
| spellingShingle | Ivan Seleznov Anton Popov Kazuhei Kikuchi Elena Kolosova Bohdan Kolomiiets Akio Nakata Miki Kaneko Ken Kiyono Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories Scientific Reports |
| title | Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories |
| title_full | Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories |
| title_fullStr | Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories |
| title_full_unstemmed | Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories |
| title_short | Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories |
| title_sort | detection of oriented fractal scaling components in anisotropic two dimensional trajectories |
| url | https://doi.org/10.1038/s41598-020-78807-z |
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