Approximating highdimensional dynamics by barycentric coordinates with linear programming
Abstract
The increasing development of novel methods and techniques facilitates the measurement of highdimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short highdimensional time series observed. Here, we propose a novel method to accurately model a highdimensional time series. Our method extends the barycentric coordinates to highdimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce freerunning timeseries predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
 Authors:
 Institute of Industrial Science, The University of Tokyo, 461 Komaba, Meguroku, Tokyo 1538505 (Japan)
 (Japan)
 Department of Mathematical Informatics, The University of Tokyo, Bunkyoku, Tokyo 1138656 (Japan)
 Center for Research in Agricultural Genomics (CRAG), Consorci CSICIRTAUABUB, Barcelona 08193 (Spain)
 Publication Date:
 OSTI Identifier:
 22403372
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ATTRACTORS; COORDINATES; DYNAMICS; ERRORS; FORECASTING; LINEAR PROGRAMMING; MANYDIMENSIONAL CALCULATIONS; MATHEMATICAL MODELS; PHASE SPACE; SIMULATION; TIMESERIES ANALYSIS; TOPOLOGY; WEATHER
Citation Formats
Hirata, Yoshito, Email: yoshito@sat.t.utokyo.ac.jp, Aihara, Kazuyuki, Suzuki, Hideyuki, Department of Mathematical Informatics, The University of Tokyo, Bunkyoku, Tokyo 1138656, CREST, JST, 418 Honcho, Kawaguchi, Saitama 3320012, Shiro, Masanori, Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 3058568, Takahashi, Nozomu, and Mas, Paloma. Approximating highdimensional dynamics by barycentric coordinates with linear programming. United States: N. p., 2015.
Web. doi:10.1063/1.4906746.
Hirata, Yoshito, Email: yoshito@sat.t.utokyo.ac.jp, Aihara, Kazuyuki, Suzuki, Hideyuki, Department of Mathematical Informatics, The University of Tokyo, Bunkyoku, Tokyo 1138656, CREST, JST, 418 Honcho, Kawaguchi, Saitama 3320012, Shiro, Masanori, Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 3058568, Takahashi, Nozomu, & Mas, Paloma. Approximating highdimensional dynamics by barycentric coordinates with linear programming. United States. doi:10.1063/1.4906746.
Hirata, Yoshito, Email: yoshito@sat.t.utokyo.ac.jp, Aihara, Kazuyuki, Suzuki, Hideyuki, Department of Mathematical Informatics, The University of Tokyo, Bunkyoku, Tokyo 1138656, CREST, JST, 418 Honcho, Kawaguchi, Saitama 3320012, Shiro, Masanori, Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 3058568, Takahashi, Nozomu, and Mas, Paloma. 2015.
"Approximating highdimensional dynamics by barycentric coordinates with linear programming". United States.
doi:10.1063/1.4906746.
@article{osti_22403372,
title = {Approximating highdimensional dynamics by barycentric coordinates with linear programming},
author = {Hirata, Yoshito, Email: yoshito@sat.t.utokyo.ac.jp and Aihara, Kazuyuki and Suzuki, Hideyuki and Department of Mathematical Informatics, The University of Tokyo, Bunkyoku, Tokyo 1138656 and CREST, JST, 418 Honcho, Kawaguchi, Saitama 3320012 and Shiro, Masanori and Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 3058568 and Takahashi, Nozomu and Mas, Paloma},
abstractNote = {The increasing development of novel methods and techniques facilitates the measurement of highdimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short highdimensional time series observed. Here, we propose a novel method to accurately model a highdimensional time series. Our method extends the barycentric coordinates to highdimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce freerunning timeseries predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.},
doi = {10.1063/1.4906746},
journal = {Chaos (Woodbury, N. Y.)},
number = 1,
volume = 25,
place = {United States},
year = 2015,
month = 1
}

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