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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/2237/00030878f5498053-96d8-40fe-be52-e4d1709d832e
名前 / ファイル | ライセンス | アクション |
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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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× Kawahara, Yoshinobu |
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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 | ||||||
内容記述タイプ | Abstract | |||||
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 | ||||||
内容記述タイプ | Other | |||||
内容記述 | ファイル公開:2021-09-01 | |||||
言語 | ja | |||||
出版者 | ||||||
出版者 | Elsevier | |||||
言語 | en | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | 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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著者版フラグ | ||||||
値 | author |