Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering
Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibilit...
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| Autor*in: |
Huang, Shih-Gu [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Neural computing & applications - Springer London, 1993, 33(2021), 20 vom: 18. Sept., Seite 13693-13704 |
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| Übergeordnetes Werk: |
volume:33 ; year:2021 ; number:20 ; day:18 ; month:09 ; pages:13693-13704 |
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| DOI / URN: |
10.1007/s00521-021-06006-6 |
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OLC2077265515 |
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| 520 | |a Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). | ||
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10.1007/s00521-021-06006-6 doi (DE-627)OLC2077265515 (DE-He213)s00521-021-06006-6-p DE-627 ger DE-627 rakwb eng 004 VZ Huang, Shih-Gu verfasserin aut Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). Graph convolutional neural network Signals on surfaces Chebyshev polynomial Hermite polynomial Laguerre polynomial Laplace–Beltrami operator. Chung, Moo K. aut Qiu, Anqi aut Enthalten in Neural computing & applications Springer London, 1993 33(2021), 20 vom: 18. Sept., Seite 13693-13704 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:33 year:2021 number:20 day:18 month:09 pages:13693-13704 https://doi.org/10.1007/s00521-021-06006-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_2018 GBV_ILN_4277 AR 33 2021 20 18 09 13693-13704 |
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10.1007/s00521-021-06006-6 doi (DE-627)OLC2077265515 (DE-He213)s00521-021-06006-6-p DE-627 ger DE-627 rakwb eng 004 VZ Huang, Shih-Gu verfasserin aut Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). Graph convolutional neural network Signals on surfaces Chebyshev polynomial Hermite polynomial Laguerre polynomial Laplace–Beltrami operator. Chung, Moo K. aut Qiu, Anqi aut Enthalten in Neural computing & applications Springer London, 1993 33(2021), 20 vom: 18. Sept., Seite 13693-13704 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:33 year:2021 number:20 day:18 month:09 pages:13693-13704 https://doi.org/10.1007/s00521-021-06006-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_2018 GBV_ILN_4277 AR 33 2021 20 18 09 13693-13704 |
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10.1007/s00521-021-06006-6 doi (DE-627)OLC2077265515 (DE-He213)s00521-021-06006-6-p DE-627 ger DE-627 rakwb eng 004 VZ Huang, Shih-Gu verfasserin aut Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). Graph convolutional neural network Signals on surfaces Chebyshev polynomial Hermite polynomial Laguerre polynomial Laplace–Beltrami operator. Chung, Moo K. aut Qiu, Anqi aut Enthalten in Neural computing & applications Springer London, 1993 33(2021), 20 vom: 18. Sept., Seite 13693-13704 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:33 year:2021 number:20 day:18 month:09 pages:13693-13704 https://doi.org/10.1007/s00521-021-06006-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_2018 GBV_ILN_4277 AR 33 2021 20 18 09 13693-13704 |
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10.1007/s00521-021-06006-6 doi (DE-627)OLC2077265515 (DE-He213)s00521-021-06006-6-p DE-627 ger DE-627 rakwb eng 004 VZ Huang, Shih-Gu verfasserin aut Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). Graph convolutional neural network Signals on surfaces Chebyshev polynomial Hermite polynomial Laguerre polynomial Laplace–Beltrami operator. Chung, Moo K. aut Qiu, Anqi aut Enthalten in Neural computing & applications Springer London, 1993 33(2021), 20 vom: 18. Sept., Seite 13693-13704 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:33 year:2021 number:20 day:18 month:09 pages:13693-13704 https://doi.org/10.1007/s00521-021-06006-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_2018 GBV_ILN_4277 AR 33 2021 20 18 09 13693-13704 |
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10.1007/s00521-021-06006-6 doi (DE-627)OLC2077265515 (DE-He213)s00521-021-06006-6-p DE-627 ger DE-627 rakwb eng 004 VZ Huang, Shih-Gu verfasserin aut Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). Graph convolutional neural network Signals on surfaces Chebyshev polynomial Hermite polynomial Laguerre polynomial Laplace–Beltrami operator. Chung, Moo K. aut Qiu, Anqi aut Enthalten in Neural computing & applications Springer London, 1993 33(2021), 20 vom: 18. Sept., Seite 13693-13704 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:33 year:2021 number:20 day:18 month:09 pages:13693-13704 https://doi.org/10.1007/s00521-021-06006-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_2018 GBV_ILN_4277 AR 33 2021 20 18 09 13693-13704 |
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Huang, Shih-Gu Chung, Moo K. Qiu, Anqi |
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revisiting convolutional neural network on graphs with polynomial approximations of laplace–beltrami spectral filtering |
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Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering |
| abstract |
Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
| abstractGer |
Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace–Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We define spectral filters via the LB operator on a graph and explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters. We then update the LB operator for pooling in the LB-CNN. We employ the brain image data from Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) to demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of two datasets, we showed that the LB-CNN slightly improves classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. The LB-CNN trained via the ADNI dataset can achieve reasonable classification accuracy for the OASIS dataset. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator). © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 |
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Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering |
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