Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911766710059008 |
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| author | Yan, Yi Peng, Changran Kuruoglu, Ercan Engin |
| author_facet | Yan, Yi Peng, Changran Kuruoglu, Ercan Engin |
| contents | The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation Yan, Yi Peng, Changran Kuruoglu, Ercan Engin Machine Learning Signal Processing The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks. |
| title | Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2401.15304 |