Simplified Energy Landscape for Modularity Using Total Variation

DOI10.1137/17M1138972zbMath1398.65133arXiv1707.09285MaRDI QIDQ4686633

Zachary M. Boyd, Egil Bae, Andrea L. Bertozzi, Xue-Cheng Tai

Publication date: 4 October 2018

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.09285

zbMATH Keywords

graphssocial networksmodularitydata clusteringcommunity detectionMBO scheme

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Clustering in the social and behavioral sciences (91C20) Social networks; opinion dynamics (91D30) Numerical optimization and variational techniques (65K10) Applications of graph theory to circuits and networks (94C15) Numerical methods of relaxation type (49M20) Ginzburg-Landau equations (35Q56)

Related Items (5)

From graph cuts to isoperimetric inequalities: convergence rates of Cheeger cuts on data clouds ⋮ Proximal gradient methods for general smooth graph total variation model in unsupervised learning ⋮ Preconditioned Algorithm for Difference of Convex Functions with Applications to Graph Ginzburg–Landau Model ⋮ Total Variation Based Community Detection Using a Nonlinear Optimization Approach ⋮ Stochastic block models are a discrete surface tension

Uses Software

• igraph
• RecPF
• MNIST
• Vlfeat
• GenLouvain

Cites Work

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• Nonlinear total variation based noise removal algorithms
• On total variation minimization and surface evolution using parametric maximum flows
• Global binary optimization on graphs for classification of high-dimensional data
• Modularity-maximizing graph communities via mathematical programming
• High resolution schemes for hyperbolic conservation laws
• An introduction to \(\Gamma\)-convergence
• \(\Gamma\)-convergence of graph Ginzburg-Landau functionals
• Mean curvature, threshold dynamics, and phase field theory on finite graphs
• Convexified modularity maximization for degree-corrected stochastic block models
• Threshold dynamics for the piecewise constant Mumford-Shah functional
• A Rayleigh-Chebyshev procedure for finding the smallest eigenvalues and associated eigenvectors of large sparse Hermitian matrices
• An MBO Scheme on Graphs for Classification and Image Processing
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Nonlocal Operators with Applications to Image Processing
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
• The Split Bregman Method for L1-Regularized Problems
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Communities in Networks
• Local minimisers and singular perturbations
• An Efficient Heuristic Procedure for Partitioning Graphs
• Active contours without edges
• Diffuse Interface Models on Graphs for Classification of High Dimensional Data
• A Total Variation Spectral Framework for Scale and Texture Analysis
• Fast unfolding of communities in large networks
• Some Facts About Operator-Splitting and Alternating Direction Methods
• A Method Based on Total Variation for Network Modularity Optimization Using the MBO Scheme
• Second-order Cone Programming Methods for Total Variation-Based Image Restoration
• Networks

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