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Multiway p-spectral graph cuts on Grassmann manifolds

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for [Formula: see text] . The problem of...

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Autores principales: Pasadakis, Dimosthenis, Alappat, Christie Louis, Schenk, Olaf, Wellein, Gerhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8948154/
https://www.ncbi.nlm.nih.gov/pubmed/35400807
http://dx.doi.org/10.1007/s10994-021-06108-1
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author Pasadakis, Dimosthenis
Alappat, Christie Louis
Schenk, Olaf
Wellein, Gerhard
author_facet Pasadakis, Dimosthenis
Alappat, Christie Louis
Schenk, Olaf
Wellein, Gerhard
author_sort Pasadakis, Dimosthenis
collection PubMed
description Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for [Formula: see text] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.
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spelling pubmed-89481542022-04-07 Multiway p-spectral graph cuts on Grassmann manifolds Pasadakis, Dimosthenis Alappat, Christie Louis Schenk, Olaf Wellein, Gerhard Mach Learn Article Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for [Formula: see text] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets. Springer US 2021-11-18 2022 /pmc/articles/PMC8948154/ /pubmed/35400807 http://dx.doi.org/10.1007/s10994-021-06108-1 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Pasadakis, Dimosthenis
Alappat, Christie Louis
Schenk, Olaf
Wellein, Gerhard
Multiway p-spectral graph cuts on Grassmann manifolds
title Multiway p-spectral graph cuts on Grassmann manifolds
title_full Multiway p-spectral graph cuts on Grassmann manifolds
title_fullStr Multiway p-spectral graph cuts on Grassmann manifolds
title_full_unstemmed Multiway p-spectral graph cuts on Grassmann manifolds
title_short Multiway p-spectral graph cuts on Grassmann manifolds
title_sort multiway p-spectral graph cuts on grassmann manifolds
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8948154/
https://www.ncbi.nlm.nih.gov/pubmed/35400807
http://dx.doi.org/10.1007/s10994-021-06108-1
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