Random walks on simplicial complexes and harmonics

In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k‐dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random wal...

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Detalles Bibliográficos
Autores principales: Mukherjee, Sayan, Steenbergen, John
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley and Sons Inc. 2016
Materias:
Research Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5324709/
https://www.ncbi.nlm.nih.gov/pubmed/28303080
http://dx.doi.org/10.1002/rsa.20645
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author Mukherjee, Sayan
Steenbergen, John
author_facet Mukherjee, Sayan
Steenbergen, John
author_sort Mukherjee, Sayan
collection PubMed
description In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k‐dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi‐supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 379–405, 2016
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spelling pubmed-53247092017-03-14 Random walks on simplicial complexes and harmonics Mukherjee, Sayan Steenbergen, John Random Struct Algorithms Research Articles In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k‐dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi‐supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 379–405, 2016 John Wiley and Sons Inc. 2016-03-07 2016-09 /pmc/articles/PMC5324709/ /pubmed/28303080 http://dx.doi.org/10.1002/rsa.20645 Text en © 2016 The Authors Random Structures & Algorithms Published by Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs (http://creativecommons.org/licenses/by-nc-nd/4.0/) License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
spellingShingle Research Articles
Mukherjee, Sayan
Steenbergen, John
Random walks on simplicial complexes and harmonics
title Random walks on simplicial complexes and harmonics
title_full Random walks on simplicial complexes and harmonics
title_fullStr Random walks on simplicial complexes and harmonics
title_full_unstemmed Random walks on simplicial complexes and harmonics
title_short Random walks on simplicial complexes and harmonics
title_sort random walks on simplicial complexes and harmonics
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5324709/
https://www.ncbi.nlm.nih.gov/pubmed/28303080
http://dx.doi.org/10.1002/rsa.20645
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