一种自适应动态模式分解方法
Towards an Adaptive Dynamic Mode Decomposition
摘要：
动态模式分解（DMD）是一种基于数据的建模工具，它识别一个矩阵，将某个时刻的量映射到未来的相同量。我们设计了一个新版本，我们称之为自适应动态模式分解（ADMD），它根据数据的性质利用时间延迟坐标，投影方法和滤波器来创建可用问题的模型。过滤器对于降低高维数据集的排名非常有效。我们采用了“离散傅里叶变换”和“增广拉格朗日乘子”作为滤波器在我们的方法。建议的ADMD进行了测试，不同的复杂性和它的性能似乎是有前途的几个数据集。
英文摘要：
Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD) that utilizes time delay coordinates, projection methods and filters as per the nature of the data to create a model for the available problem. Filters are very effective in reducing the rank of high-dimensional dataset. We have incorporated 'discrete Fourier transform' and 'augmented lagrangian multiplier' as filters in our method. The proposed ADMD is tested on several datasets of varying complexities and its performance appears to be promising.
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