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  1. A500 情報学部/情報学研究科・情報文化学部・情報科学研究科
  2. A500a 雑誌掲載論文
  3. 学術雑誌

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

http://hdl.handle.net/2237/00030878
http://hdl.handle.net/2237/00030878
f5498053-96d8-40fe-be52-e4d1709d832e
名前 / ファイル ライセンス アクション
1808_10551.pdf 1808_10551 (4.9 MB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2019-11-14
タイトル
タイトル Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables
言語 en
著者 Fujii, Keisuke

× Fujii, Keisuke

WEKO 94165

en Fujii, Keisuke

Search repository
Kawahara, Yoshinobu

× Kawahara, Yoshinobu

WEKO 94166

en Kawahara, Yoshinobu

Search repository
アクセス権
アクセス権 open access
アクセス権URI http://purl.org/coar/access_right/c_abf2
権利
言語 en
権利情報 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
キーワード
主題Scheme Other
主題 Dynamical systems
キーワード
主題Scheme Other
主題 Dimensionality reduction
キーワード
主題Scheme Other
主題 Spectral analysis
キーワード
主題Scheme Other
主題 Unsupervised learning
抄録
内容記述 Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.
言語 en
内容記述タイプ Abstract
内容記述
内容記述 ファイル公開:2021-09-01
言語 ja
内容記述タイプ Other
出版者
言語 en
出版者 Elsevier
言語
言語 eng
資源タイプ
資源タイプresource http://purl.org/coar/resource_type/c_6501
タイプ journal article
出版タイプ
出版タイプ AM
出版タイプResource http://purl.org/coar/version/c_ab4af688f83e57aa
DOI
関連タイプ isVersionOf
識別子タイプ DOI
関連識別子 https://doi.org/10.1016/j.neunet.2019.04.020
ISSN(print)
収録物識別子タイプ PISSN
収録物識別子 0893-6080
書誌情報 en : Neural Networks

巻 117, p. 94-103, 発行日 2019-09
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