Related papers: Data-driven Signal Decomposition Approaches: A Com…
The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decomposition methods led by the empirical mode decomposition, which was…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…
We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…
Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…
The Ensemble Empirical Mode Decomposition (EEMD) has become a preferred technique to decompose nonlinear and non-stationary signals due to its ability to create time-varying basis functions. However, current EEMD signal cleaning techniques…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis,…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…
This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…