Supervised dynamic mode decomposition via multitask learning
Supervised dynamic mode decomposition via multitask learning
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DOI：
10.1016/j.patrec.2019.02.010
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Keisuke Fujii;Y. Kawahara
中科院分区：
文献类型：
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作者：
Keisuke Fujii;Y. Kawahara
通过从数据中提取时空模式来理解动力系统是工程和科学各个领域的基础。动态模式分解（DMD）最近引起了这些领域的关注，作为一种从数据中获得非线性动力系统的全局模态描述的方式，而不需要显式的先验知识。然而，DMD原则上是一种无监督的降维算法，即使给定一组具有不同标签的数据，它也不具有利用标签信息的机制。在本文中，我们提出的算法，将标签信息到DMD通过多任务学习解决稀疏群Lasso。为此，我们通过将具有不同标签的数据视为不同的任务，以标签方式估计动态模式上的稀疏权重。通过这种方法估计的模态描述共享一部分全局模态，从而提取标签特定的和共同的（或混合的）动力学结构，这可能有助于理解数据背后的时空行为机制。我们使用合成和真实世界的数据集调查的经验性能，并验证我们的算法可以提取和可视化常见的和标签特定的时空结构。
Understanding dynamical systems by extracting spatiotemporal patterns from data is fundamental in a variety of fields of engineering and science. Dynamic mode decomposition (DMD) has recently attracted attention in these fields as a way of obtaining a global modal description of a nonlinear dynamical system from data, without requiring explicit prior knowledge. However, DMD is in principle an unsupervised dimensionality reduction algorithm; it is not endowed with the mechanism to utilize label information even if a set of data with different labels is given. In this paper, we propose the algorithm that incorporates label information into DMD via multitask learning by solving sparse-group Lasso. To this end, we estimate sparse weights over dynamic modes in a label-wise manner by regarding data with different labels as different tasks. Modal descriptions estimated by this approach share a part of the global modes, resulting in the extraction of label-specific and common (or mixed) dynamical structures, which could be useful in understanding mechanisms in the spatiotemporal behavior behind data. We investigate the empirical performance using synthetic and real-world datasets, and validate that our algorithm can extract and visualize common and label-specific spatiotemporal structures.