Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide a systematic advancement of these and examine the interrelations. In addition, several results of each variant are proven. Our main result is the exact reconstruction property. To this end, a new modification of scaling factors is presented and a new concept of an error scaling is introduced to guarantee an error-free reconstruction of the data.
翻译：动态模式分解(DMD)是一种数据驱动的分解技术,它提取了时间依赖现象的时空模式。在本文件中,我们对DMD的各种变体进行全面的理论分析。我们系统地推进这些变体,并检查它们之间的相互关系。此外,每个变体的一些结果都得到了证明。我们的主要结果就是确切的重建属性。为此,提出了对缩放因子进行新的修改,并引入了一种错误缩放的新概念,以保证数据的无误重建。
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