title: Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
abstract: The increasing development of novel methods and techniques facilitates the measurement of high-dimensional 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 high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series 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, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
authors: Yoshito
authors: Y
authors: Hirata
authors: Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors: Masanori
authors: M
authors: Shiro
authors: Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193, Spain.
authors: Nozomu
authors: N
authors: Takahashi
authors: Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
authors: Kazuyuki
authors: K
authors: Aihara
authors: Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
authors: Hideyuki
authors: H
authors: Suzuki
authors: Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193, Spain.
authors: Paloma
authors: P
authors: Mas