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SRMD: Sparse Random Mode Decomposition
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for...
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Stochastic Parameterization with Dynamic Mode Decomposition
A physical stochastic parameterization is adopted in this work to account for the effects of the unresolved small-scale on the large-scale flow...
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Kernel Mode Decomposition and the Programming of Kernels
This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve...
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Embedded Platform-Based Heart-Lung Sound Separation Using Variational Mode Decomposition
Cardiovascular diseases (CVD) are often identified by the audio characteristics of persistent heart and lung sounds of healthy and abnormal subjects....
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Low-Rank Dynamic Mode Decomposition: An Exact and Tractable Solution
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition. Searching this...
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Kernel Mode Decomposition Networks (KMDNets)
In this chapter, we describe kernel mode decomposition networks (KMDNets) as a powerful development of the previous chapter. Indeed, the recovery...
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Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection
In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to...
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TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization
This paper proposes an algorithm based on defined scaled tri-factorization (STF) for fast and accurate tensor ring (TR) decomposition. First, based...
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A block-randomized stochastic method with importance sampling for CP tensor decomposition
One popular way to compute the CANDECOMP/PARAFAC (CP) decomposition of a tensor is to transform the problem into a sequence of overdetermined least...
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Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format
The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are...
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Tensor Completion via A Generalized Transformed Tensor T-Product Decomposition Without t-SVD
Matrix and tensor nuclear norms have been successfully used to promote the low-rankness of tensors in low-rank tensor completion. However, singular...
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Empirical CERTs
The potential role that CERT can play in rejuvenating the human brain functionality following the pathophysiology of neurodegenerative diseases is...
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Learning Proper Orthogonal Decomposition of Complex Dynamics Using Heavy-ball Neural ODEs
Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high...
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Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition
As planetary flows are characterised by interaction of phenomenons in a huge range of scales, it is unaffordable today to resolve numerically the...
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Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition
Many tasks in real life scenarios can be naturally formulated as nonconvex optimization problems. Unfortunately, to date, the iterative numerical...
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Tensor Completion via Fully-Connected Tensor Network Decomposition with Regularized Factors
The recently proposed fully-connected tensor network (FCTN) decomposition has a powerful ability to capture the low-rankness of tensors and has...
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Hybrid CUR-type decomposition of tensors in the Tucker format
The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a...
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Hankel tensor-based model and \(L_1\)-Tucker decomposition-based frequency recovery method for harmonic retrieval problem
Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have...
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Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data
U -statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U -statistics...
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Dynamic Mode Decomposition: A Tool to Extract Structures Hidden in Massive Datasets
Dynamic Mode Decomposition (DMD) is able to decompose flow field data into coherent modes and determine their oscillatory frequencies and...