A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs

Zheng, Xianwei; Tang, Yuan Yan; Zhou, Jiantao

doi:10.1109/tsp.2019.2896246

Cited by 125 publications

(45 citation statements)

References 38 publications

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“…Several methods have been used to solve (), for example, the existence of a positive ground state solution was obtained by Poppenberg et al 1 (resp., Liu et al 10 ) with the help of the constrained minimization argument (resp., perturbation approach); by a change of variables (dual approach) the quasilinear problem was transformed to a semilinear one 11,12 ; the existence of ground state solution was established 13,14 by means of the Nehari method. It is worth mentioning that wavelet‐fractal techniques have been widely used to find numerical solutions of nonlinear (fractional) Schrödinger equation, we refer the reader to previous studies 15–20 and references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

Wei

Yang

et al. 2021

Math Methods in App Sciences

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In this paper, we study the following quasilinear Schrödinger equations −Δu−Δ(|u|2α)|u|2α−2u=ω(x)|u|q−1u,x∈ℝN, where α>12 is a parameter, q>3α−1+α2α, ωfalse(xfalse)∈Cfalse(ℝN\false{0false}false) is a positive function. We establish a Liouville type theorem for the class of stable bounded sign‐changing solutions under suitable assumptions on ω(x), q, α and N.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

Wei

Yang

et al. 2021

Math Methods in App Sciences

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“…Involving the heuristic algorithms, the Nawaz-Enscore-Ham (NEH) algorithm employed by Nawaz et al [9] for solving PFSSP could be the most effective heuristic algorithm, and their results are comparable with the meta-heuristic algorithms [10][11][12][13], which are being used for solving several optimization problems in a reasonable time. Broadly speaking, the image segmentation problem is an indispensable process in image processing fields, so several image segmentation methods have been suggested such as clustering, fractal-wavelet techniques [14][15][16][17][18][19][20], region growing, and thresolding; Among those techniques, the threshold-based segmentation technique is the most effective due to the metaheuristic algorithms which could segment the images based on this technique with high accuracy [21].…”

Section: Of 24mentioning

confidence: 99%

A Local Search-Based Generalized Normal Distribution Algorithm for Permutation Flow Shop Scheduling

et al. 2021

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This paper studies the generalized normal distribution algorithm (GNDO) performance for tackling the permutation flow shop scheduling problem (PFSSP). Because PFSSP is a discrete problem and GNDO generates continuous values, the largest ranked value rule is used to convert those continuous values into discrete ones to make GNDO applicable for solving this discrete problem. Additionally, the discrete GNDO is effectively integrated with a local search strategy to improve the quality of the best-so-far solution in an abbreviated version of HGNDO. More than that, a new improvement using the swap mutation operator applied on the best-so-far solution to avoid being stuck into local optima by accelerating the convergence speed is effectively applied to HGNDO to propose a new version, namely a hybrid-improved GNDO (HIGNDO). Last but not least, the local search strategy is improved using the scramble mutation operator to utilize each trial as ideally as possible for reaching better outcomes. This improved local search strategy is integrated with IGNDO to produce a new strong algorithm abbreviated as IHGNDO. Those proposed algorithms are extensively compared with a number of well-established optimization algorithms using various statistical analyses to estimate the optimal makespan for 41 well-known instances in a reasonable time. The findings show the benefits and speedup of both IHGNDO and HIGNDO over all the compared algorithms, in addition to HGNDO.

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“…Unsigned complex networks can be modeled as a graph G = (V,E). In graph, V represents the set of nodes and E represents the set of edges [28]. An A matrix represents the node interconnections.…”

Section: A Complex Network Definitionmentioning

confidence: 99%

Multiobjective Complex Network Clustering Based on Dynamical Decomposition Particle Swarm Optimization

2020

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Clustering is a basic tool applied to complex networks. However, the clustering of complex networks is often based on a single objective function, which can obtain insufficient clustering effects. To address the insufficiencies of single objective complex network clustering, multiobjective complex network clustering was proposed. In this article, to improve multiobjective complex network clustering, we prove the superiority of dynamic decomposition mathematically and propose a parallel discrete particle swarm optimization algorithm based on dynamic decomposition (DDDPSO). First, solutions are obtained at different levels by optimizing the objective functions of parallel subpopulations. Second, the decomposition space is divided dynamically by the reference vector of dynamic decomposition. Particle swarms are used to search for optimal solutions in the partitioned dynamic spaces. Finally, the individuals in the particle swarm are sorted according to the obtained solutions to obtain individuals with good convergence and diversity. We conduct comparisons with many state-of-the-art algorithms on many widely used test datasets to test the DDDPSO. The experimental results show the effectiveness of the proposed approach for complex network clustering. INDEX TERMS Multiobjective optimization, complex network clustering, discrete particle swarm, dynamic decomposition.

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A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs

Cited by 125 publications

References 38 publications

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

A Local Search-Based Generalized Normal Distribution Algorithm for Permutation Flow Shop Scheduling

Multiobjective Complex Network Clustering Based on Dynamical Decomposition Particle Swarm Optimization

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