The Nonlocal p-Laplacian Evolution Problem on Graphs: The Continuum Limit

Hafiene, Yosra; Fadili, Jalal M.; Elmoataz, Abderrahim

doi:10.1007/978-3-319-94211-7_40

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…εn,con (f ; ρ) was considered in [61] as an intermediary functional to provide convergence between E (p) n,con (f ) and E (p) ∞,con and has appeared in [30][31][32] as the continuum limit of E (p) n,con when ε n = ε is fixed (although not using the hard constraint). We also develop a numerical method for computing minimisers of the above functional that are efficient for large n.…”

Section: Introductionmentioning

confidence: 99%

PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds

Crook¹,

Hurst²,

Schönlieb³

et al. 2019

Preprint

View full text Add to dashboard Cite

Given a data set and a subset of labels the problem of semi-supervised learning on point clouds is to extend the labels to the entire data set. In this paper we extend the labels by minimising the constrained discrete p-Dirichlet energy. Under suitable conditions the discrete problem can be connected, in the large data limit, with the minimiser of a weighted continuum p-Dirichlet energy with the same constraints. We take advantage of this connection by designing numerical schemes that first estimate the density of the data and then apply PDE methods, such as pseudo-spectral methods, to solve the corresponding Euler-Lagrange equation. We prove that our scheme is consistent in the large data limit for two methods of density estimation: kernel density estimation and spline kernel density estimation.

show abstract