Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations
A lot of works have shown that frobenius-norm-based representation (FNR) is competitive to sparse representation and nuclear-norm-based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to und...
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| Veröffentlicht in: | IEEE transaction on neural networks and learning systems 2018-01, Vol.29 (1), p.218-224 |
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| creator | Peng, Xi Lu, Canyi Yi, Zhang Tang, Huajin |
| description | A lot of works have shown that frobenius-norm-based representation (FNR) is competitive to sparse representation and nuclear-norm-based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this brief, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption and 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary. |
| doi_str_mv | 10.1109/TNNLS.2016.2608834 |
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More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption and 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.</description><identifier>ISSN: 2162-237X</identifier><identifier>EISSN: 2162-2388</identifier><identifier>DOI: 10.1109/TNNLS.2016.2608834</identifier><identifier>PMID: 27723605</identifier><identifier>CODEN: ITNNAL</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>Artificial neural networks ; Clustering ; Corruption ; Dictionaries ; equivalence ; Gaussian noise ; Laplace equations ; Learning systems ; least square regression ; Linear programming ; low rank representation (LRR) ; Minimization ; Noise ; rank minimization ; Representations ; Theoretical analysis ; ℓ₂-minimization</subject><ispartof>IEEE transaction on neural networks and learning systems, 2018-01, Vol.29 (1), p.218-224</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Artificial neural networks Clustering Corruption Dictionaries equivalence Gaussian noise Laplace equations Learning systems least square regression Linear programming low rank representation (LRR) Minimization Noise rank minimization Representations Theoretical analysis ℓ₂-minimization |
| title | Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations |
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