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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.00004 |
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| _version_ | 1866911769268584448 |
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| author | Zhu, Hongyu Klus, Stefan Sahai, Tuhin |
| author_facet | Zhu, Hongyu Klus, Stefan Sahai, Tuhin |
| contents | We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph. However, instead of using a fast Fourier transform (FFT) computation at every node, our proposed approach exploits the Koopman operator framework. Specifically, we show that propagating waves in the graph followed by a local dynamic mode decomposition (DMD) computation at every node is capable of retrieving the eigenvalues and the local eigenvector components of the graph Laplacian, thereby providing local cluster assignments for all nodes. We demonstrate that the DMD computation is more robust than the existing FFT based approach and requires 20 times fewer steps of the wave equation to accurately recover the clustering information and reduces the relative error by orders of magnitude. We demonstrate the decentralized approach on a range of graph clustering problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_00004 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Dynamic Mode Decomposition Approach for Decentralized Spectral Clustering of Graphs Zhu, Hongyu Klus, Stefan Sahai, Tuhin Machine Learning Distributed, Parallel, and Cluster Computing Discrete Mathematics We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph. However, instead of using a fast Fourier transform (FFT) computation at every node, our proposed approach exploits the Koopman operator framework. Specifically, we show that propagating waves in the graph followed by a local dynamic mode decomposition (DMD) computation at every node is capable of retrieving the eigenvalues and the local eigenvector components of the graph Laplacian, thereby providing local cluster assignments for all nodes. We demonstrate that the DMD computation is more robust than the existing FFT based approach and requires 20 times fewer steps of the wave equation to accurately recover the clustering information and reduces the relative error by orders of magnitude. We demonstrate the decentralized approach on a range of graph clustering problems. |
| title | A Dynamic Mode Decomposition Approach for Decentralized Spectral Clustering of Graphs |
| topic | Machine Learning Distributed, Parallel, and Cluster Computing Discrete Mathematics |
| url | https://arxiv.org/abs/2203.00004 |