Strong consistency of the projected total least squares dynamic mode decomposition for datasets with random noise
Strong consistency of the projected total least squares dynamic mode decomposition for datasets with random noise
复制标题
随机噪声数据集投影总最小二乘动态模式分解的强一致性
DOI：
10.1007/s13160-022-00547-6
复制
发表时间：
2022
影响因子：
0.9
通讯作者：
Kensuke Aishima
中科院分区：
文献类型：
--
作者：
向井信彦;松友悠太郎;森紀美江;武井良子;山田紘子;山下夕香里;長谷川和子;Kensuke Aishima;Takeshi Fukaya;Kensuke Aishima
动态模式分解（DMD）作为时间序列数据的分析方法近年来备受关注。在本文中，我们对DMD进行渐近分析，以证明统计意义上的强一致性。更具体地说，我们首先给出具有观测噪声的数据的随机噪声统计模型。在 DMD 的许多变体中，总体最小二乘 DMD (TLS-DMD) 被认为是观测中随机噪声的稳健方法。我们专注于统计意义上的 TLS-DMD 一致性分析，旨在推广预测方法的分析。本文给出了基于类比统计模型下的适当正交分解的高效降维的投影方法设计的总体框架，并证明了其估计的强一致性。
Dynamic mode decomposition (DMD) has attracted much attention in recent years as an analysis method for time series data. In this paper, we perform asymptotic analysis on the DMD to prove strong consistency in the statistical sense. More specifically, we first give a statistical model of random noise for data with observation noise. Among many variants of the DMD, the total least squares DMD (TLS-DMD) is known as a robust method for the random noise in the observation. We focus on consistency analysis of the TLS-DMD in the statistical sense and aim to generalize the analysis for projected methods. This paper gives a general framework for designing projection methods based on efficient dimensionality reduction analogously to the proper orthogonal decomposition under the statistical model and proves its strong consistency of the estimation.