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Perhaps surprisingly, the total electron microscopy (EM) data collected to date is less than a cubic millimeter. Consequently, there is an enormous demand in the materials and biological sciences to image at greater speed and lower dosage,…

This study applies Empirical Mode Decomposition (EMD) to the MSCI World index and converts the resulting intrinsic mode functions (IMFs) into graph representations to enable modeling with graph neural networks (GNNs). Using CEEMDAN, we…

Since Huang proposed the Empirical Mode Decomposition (EMD) in 1998, mode decomposition has been widely studied, but EMD and relative developed algorithms are still generally lack of adaptability and mathematical theory. This paper propose…

Nowadays, the deployment of deep learning models on edge devices for addressing real-world classification problems is becoming more prevalent. Moreover, there is a growing popularity in the approach of early classification, a technique that…

Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…

An efficient method is introduced in this paper to find the intrinsic mode function (IMF) components of time series data. This method is faster and more predictable than the Empirical Mode Decomposition (EMD) method devised by the author of…

In this study, the Multivariate Empirical Mode Decomposition (MEMD) is applied to multichannel EEG to obtain scale-aligned intrinsic mode functions (IMFs) as input features for emotion detection. The IMFs capture local signal variation…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Micro-expressions (MEs) are brief, involuntary facial movements that reveal genuine emotions, typically lasting less than half a second. Recognizing these subtle expressions is critical for applications in psychology, security, and…

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…

Regime shifts in high-dimensional time series arise naturally in many applications, from neuroimaging to finance. This problem has received considerable attention in low-dimensional settings, with both Bayesian and frequentist methods used…

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time…

The analysis of non-stationary time-series data requires insight into its local and global patterns with physical interpretability. However, traditional smoothing algorithms, such as B-splines, Savitzky-Golay filtering, and Empirical Mode…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Micro-expression recognition can obtain the real emotion of the individual at the current moment. Although deep learning-based methods, especially Transformer-based methods, have achieved impressive results, these methods have high…

Expectation Propagation (EP)-based Multiple-Input Multiple-Output (MIMO) detector is regarded as a state-of-the-art MIMO detector because of its exceptional performance. However, we find that the EP MIMO detector cannot guarantee to achieve…

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

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 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…

This paper proposes the \emph{multiresolution mode decomposition} as a novel model for adaptive time series analysis. The main conceptual innovation is the introduction of the \emph{multiresolution intrinsic mode function} (MIMF) of the…