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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…
The classical EMD algorithm has been used extensively in the literature to decompose signals that contain nonlinear waves. However when a signal contain two or more frequencies that are close to one another the decomposition might fail. In…
The Empirical Mode Decomposition (EMD) is a signal analysis method that separates multi-component signals into single oscillatory modes called intrinsic mode functions (IMFs), each of which can generally be associated to a physical meaning…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
Empirical Mode Decomposition is an adaptive and local tool that extracts underlying analytical components of a non-linear and non-stationary process, in turn, is the basis of Hilbert Huang transform, however, there are problems such as…
Cardiovascular disease is a major life-threatening condition that is commonly monitored using electrocardiogram (ECG) signals. However, these signals are often contaminated by various types of noise at different intensities, significantly…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
An extreme-point symmetric mode decomposition (ESMD) method is proposed to improve the Hilbert-Huang Transform (HHT) through the following prospects: (1) The sifting process is implemented by the aid of 1, 2, 3 or more inner interpolating…
The Blaschke decomposition-based algorithm, {\em Phase Dynamics Unwinding} (PDU), possesses several attractive theoretical properties, including fast convergence, effective decomposition, and multiscale analysis. However, its application to…
This article addresses extraction of physically meaningful information from STEM EELS and EDX spectrum-images using methods of Multivariate Statistical Analysis. The problem is interpreted in terms of data distribution in a…
In this paper a signal denoising scheme based on Empirical mode decomposition (EMD) is presented. The denoising method is a fully data driven approach. Noisy signal is decomposed adaptively into intrinsic oscillatory components called…
Traffic flow forecasting is a crucial task in intelligent transport systems. Deep learning offers an effective solution, capturing complex patterns in time-series traffic flow data to enable the accurate prediction. However, deep learning…
Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
The classical EMD algorithm has been used extensively in the literature to decompose signals that contain nonlinear waves. However when a signal contain two or more frequencies that are close to one another the decomposition might fail. In…
We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the…
Time series anomaly detection is crucial for maintaining stable systems. Existing methods face two main challenges. First, it is difficult to directly model the dependencies of diverse and complex patterns within the sequences. Second, many…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…