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Article: Locality-preserving low-rank representation for graph construction from nonlinear manifolds

TitleLocality-preserving low-rank representation for graph construction from nonlinear manifolds
Authors
KeywordsGraph construction
Low-rank representation
Nonlinear manifold clustering
Issue Date2015
Citation
Neurocomputing, 2015, v. 175, n. PartA, p. 715-722 How to Cite?
AbstractBuilding a good graph to represent data structure is important in many computer vision and machine learning tasks such as recognition and clustering. This paper proposes a novel method to learn an undirected graph from a mixture of nonlinear manifolds via Locality-Preserving Low-Rank Representation (L2R2), which extents the original LRR model from linear subspaces to nonlinear manifolds. By enforcing a locality-preserving sparsity constraint to the LRR model, L2R2 guarantees its linear representation to be nonzero only in a local neighborhood of the data point, and thus preserves the intrinsic geometric structure of the manifolds. Its numerical solution results in a constrained convex optimization problem with linear constraints. We further apply a linearized alternating direction method to solve the problem. We have conducted extensive experiments to benchmark its performance against six state-of-the-art algorithms. Using nonlinear manifold clustering and semi-supervised classification on images as examples, the proposed method significantly outperforms the existing methods, and is also robust to moderate data noise and outliers.
Persistent Identifierhttp://hdl.handle.net/10722/327070
ISSN
2023 Impact Factor: 5.5
2023 SCImago Journal Rankings: 1.815
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZhuang, Liansheng-
dc.contributor.authorWang, Jingjing-
dc.contributor.authorLin, Zhouchen-
dc.contributor.authorYang, Allen Y.-
dc.contributor.authorMa, Yi-
dc.contributor.authorYu, Nenghai-
dc.date.accessioned2023-03-31T05:28:35Z-
dc.date.available2023-03-31T05:28:35Z-
dc.date.issued2015-
dc.identifier.citationNeurocomputing, 2015, v. 175, n. PartA, p. 715-722-
dc.identifier.issn0925-2312-
dc.identifier.urihttp://hdl.handle.net/10722/327070-
dc.description.abstractBuilding a good graph to represent data structure is important in many computer vision and machine learning tasks such as recognition and clustering. This paper proposes a novel method to learn an undirected graph from a mixture of nonlinear manifolds via Locality-Preserving Low-Rank Representation (L2R2), which extents the original LRR model from linear subspaces to nonlinear manifolds. By enforcing a locality-preserving sparsity constraint to the LRR model, L2R2 guarantees its linear representation to be nonzero only in a local neighborhood of the data point, and thus preserves the intrinsic geometric structure of the manifolds. Its numerical solution results in a constrained convex optimization problem with linear constraints. We further apply a linearized alternating direction method to solve the problem. We have conducted extensive experiments to benchmark its performance against six state-of-the-art algorithms. Using nonlinear manifold clustering and semi-supervised classification on images as examples, the proposed method significantly outperforms the existing methods, and is also robust to moderate data noise and outliers.-
dc.languageeng-
dc.relation.ispartofNeurocomputing-
dc.subjectGraph construction-
dc.subjectLow-rank representation-
dc.subjectNonlinear manifold clustering-
dc.titleLocality-preserving low-rank representation for graph construction from nonlinear manifolds-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.neucom.2015.10.119-
dc.identifier.scopuseid_2-s2.0-84947461329-
dc.identifier.volume175-
dc.identifier.issuePartA-
dc.identifier.spage715-
dc.identifier.epage722-
dc.identifier.eissn1872-8286-
dc.identifier.isiWOS:000367756600069-

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