A Gradient System for Low Rank Matrix Completion
In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frob...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-07-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/3/51 |
| _version_ | 1819063139957735424 |
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| author | Carmela Scalone Nicola Guglielmi |
| author_facet | Carmela Scalone Nicola Guglielmi |
| author_sort | Carmela Scalone |
| collection | DOAJ |
| description | In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature. |
| first_indexed | 2024-12-21T15:09:56Z |
| format | Article |
| id | doaj.art-715e4e11f59e4b77aae412cde12c0642 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-21T15:09:56Z |
| publishDate | 2018-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-715e4e11f59e4b77aae412cde12c06422022-12-21T18:59:18ZengMDPI AGAxioms2075-16802018-07-01735110.3390/axioms7030051axioms7030051A Gradient System for Low Rank Matrix CompletionCarmela Scalone0Nicola Guglielmi1Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica (DISIM), Università dell’Aquila, via Vetoio 1, 67100 L’Aquila, ItalySection of Mathematics, Gran Sasso Science Institute, via Crispi 7, 67100 L’Aquila, ItalyIn this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature.http://www.mdpi.com/2075-1680/7/3/51low rank completionmatrix ODEsgradient system |
| spellingShingle | Carmela Scalone Nicola Guglielmi A Gradient System for Low Rank Matrix Completion Axioms low rank completion matrix ODEs gradient system |
| title | A Gradient System for Low Rank Matrix Completion |
| title_full | A Gradient System for Low Rank Matrix Completion |
| title_fullStr | A Gradient System for Low Rank Matrix Completion |
| title_full_unstemmed | A Gradient System for Low Rank Matrix Completion |
| title_short | A Gradient System for Low Rank Matrix Completion |
| title_sort | gradient system for low rank matrix completion |
| topic | low rank completion matrix ODEs gradient system |
| url | http://www.mdpi.com/2075-1680/7/3/51 |
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