Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks
Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy fu...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kuang, Yin [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
Closed affine subspace learning (CASL) Non-negative matrix factorization (NMF) |
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| Anmerkung: |
© Springer-Verlag London 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Pattern analysis and applications - Springer London, 1998, 18(2014), 4 vom: 09. Mai, Seite 817-828 |
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| Übergeordnetes Werk: |
volume:18 ; year:2014 ; number:4 ; day:09 ; month:05 ; pages:817-828 |
| Links: |
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| DOI / URN: |
10.1007/s10044-014-0370-1 |
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OLC2051700257 |
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| 520 | |a Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. | ||
| 650 | 4 | |a Closed affine subspace learning (CASL) | |
| 650 | 4 | |a Non-negative matrix factorization (NMF) | |
| 650 | 4 | |a Sparse representation | |
| 650 | 4 | |a Multiple manifolds clustering and embedding | |
| 650 | 4 | |a Lotka–Volterra recurrent neural networks (LV RNNs) | |
| 700 | 1 | |a Zhang, Lei |4 aut | |
| 700 | 1 | |a Yi, Zhang |4 aut | |
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10.1007/s10044-014-0370-1 doi (DE-627)OLC2051700257 (DE-He213)s10044-014-0370-1-p DE-627 ger DE-627 rakwb eng 004 600 VZ 54.74$jMaschinelles Sehen bkl Kuang, Yin verfasserin aut Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2014 Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. Closed affine subspace learning (CASL) Non-negative matrix factorization (NMF) Sparse representation Multiple manifolds clustering and embedding Lotka–Volterra recurrent neural networks (LV RNNs) Zhang, Lei aut Yi, Zhang aut Enthalten in Pattern analysis and applications Springer London, 1998 18(2014), 4 vom: 09. Mai, Seite 817-828 (DE-627)24992921X (DE-600)1446989-3 (DE-576)27655583X 1433-7541 nnns volume:18 year:2014 number:4 day:09 month:05 pages:817-828 https://doi.org/10.1007/s10044-014-0370-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 54.74$jMaschinelles Sehen VZ 10641030X (DE-625)10641030X AR 18 2014 4 09 05 817-828 |
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10.1007/s10044-014-0370-1 doi (DE-627)OLC2051700257 (DE-He213)s10044-014-0370-1-p DE-627 ger DE-627 rakwb eng 004 600 VZ 54.74$jMaschinelles Sehen bkl Kuang, Yin verfasserin aut Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2014 Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. Closed affine subspace learning (CASL) Non-negative matrix factorization (NMF) Sparse representation Multiple manifolds clustering and embedding Lotka–Volterra recurrent neural networks (LV RNNs) Zhang, Lei aut Yi, Zhang aut Enthalten in Pattern analysis and applications Springer London, 1998 18(2014), 4 vom: 09. Mai, Seite 817-828 (DE-627)24992921X (DE-600)1446989-3 (DE-576)27655583X 1433-7541 nnns volume:18 year:2014 number:4 day:09 month:05 pages:817-828 https://doi.org/10.1007/s10044-014-0370-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 54.74$jMaschinelles Sehen VZ 10641030X (DE-625)10641030X AR 18 2014 4 09 05 817-828 |
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10.1007/s10044-014-0370-1 doi (DE-627)OLC2051700257 (DE-He213)s10044-014-0370-1-p DE-627 ger DE-627 rakwb eng 004 600 VZ 54.74$jMaschinelles Sehen bkl Kuang, Yin verfasserin aut Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2014 Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. Closed affine subspace learning (CASL) Non-negative matrix factorization (NMF) Sparse representation Multiple manifolds clustering and embedding Lotka–Volterra recurrent neural networks (LV RNNs) Zhang, Lei aut Yi, Zhang aut Enthalten in Pattern analysis and applications Springer London, 1998 18(2014), 4 vom: 09. Mai, Seite 817-828 (DE-627)24992921X (DE-600)1446989-3 (DE-576)27655583X 1433-7541 nnns volume:18 year:2014 number:4 day:09 month:05 pages:817-828 https://doi.org/10.1007/s10044-014-0370-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 54.74$jMaschinelles Sehen VZ 10641030X (DE-625)10641030X AR 18 2014 4 09 05 817-828 |
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constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks |
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Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks |
| abstract |
Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. © Springer-Verlag London 2014 |
| abstractGer |
Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. © Springer-Verlag London 2014 |
| abstract_unstemmed |
Abstract In this paper, the problem that we are interested is constructing $$l_{1}$$-graphs for subspace learning via recurrent neural networks. We propose a closed affine subspace learning (CASL) method to do so. The problem of CASL is formulated as an optimization problem described by an energy function in the non-negative orthant. The sufficient conditions for keeping the minimum points of the energy function in the non-negative orthant are given. A model of Lotka–Volterra recurrent neural networks is constructed to solve the optimization problem in terms of these sufficient conditions. It shows that the set of stable attractors of the network model just equals the set of minimum points of the energy function in the non-negative orthant. Based on these equivalences, the problem of CASL can be solved by running the proposed LV RNNs to obtain the stable attractors. The $$l_{1}$$-graphs then can be constructed. Experiments on some synthetic and real data show that the $$l_{1}$$-graphs constructed in this way are more effective, especially when processing the data sampled from multiple manifolds. © Springer-Verlag London 2014 |
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| title_short |
Constructing $$L_{1}$$-graphs for subspace learning via recurrent neural networks |
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https://doi.org/10.1007/s10044-014-0370-1 |
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| author2 |
Zhang, Lei Yi, Zhang |
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Zhang, Lei Yi, Zhang |
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