NDLI: Minimal Dirichlet Energy Partitions for Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Oudet, Édouard Osting, Braxton White, Chris D.
Copyright Year	2014
Abstract	Motivated by a geometric problem, we introduce a new nonconvex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel rearrangement algorithm is proposed, which we show is strictly decreasing and converges in a finite number of iterations to a local minimum of the relaxed objective function. Our method is applied to several clustering problems on graphs constructed from synthetic data, MNIST handwritten digits, and manifold discretizations. The model has a semisupervised extension and provides a natural representative for the clusters as well.
Starting Page	A1635
Ending Page	A1651
Page Count	17
File Format	PDF
ISSN	10648275
DOI	10.1137/130934568
e-ISSN	10957197
Issue Number	4
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-08-05
Access Restriction	Subscribed
Subject Keyword	semisupervised algorithm graph partition Dirichlet eigenvalues Numerical methods for variational inequalities and related problems Optimization of shapes other than minimal surfaces clustering Numerical approximation and computational geometry graph Laplacian nonnegative matrix factorization Variational methods for eigenvalues of operators rearrangement algorithm
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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