Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912018870566912 |
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| author | Nguyen, Duc Thien Slavakis, Konstantinos Pados, Dimitris |
| author_facet | Nguyen, Duc Thien Slavakis, Konstantinos Pados, Dimitris |
| contents | This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex arguments and Hodge Laplacians to incorporate the graph topology, and exploits manifold-learning arguments to identify latent geometries within features which are modeled as a point-cloud around a smooth manifold embedded in a reproducing kernel Hilbert space (RKHS). Following the concept of tangent spaces to smooth manifolds, linear approximating patches are used to add a collaborative-filtering flavor to the point-cloud approximations. Together with matrix factorizations, MultiL-KRIM effects dimensionality reduction, and enables efficient computations, without any training data or additional information. Numerical tests on real-network time-varying edge flows demonstrate noticeable improvements of MultiL-KRIM over several state-of-the-art schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning Nguyen, Duc Thien Slavakis, Konstantinos Pados, Dimitris Machine Learning Signal Processing This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex arguments and Hodge Laplacians to incorporate the graph topology, and exploits manifold-learning arguments to identify latent geometries within features which are modeled as a point-cloud around a smooth manifold embedded in a reproducing kernel Hilbert space (RKHS). Following the concept of tangent spaces to smooth manifolds, linear approximating patches are used to add a collaborative-filtering flavor to the point-cloud approximations. Together with matrix factorizations, MultiL-KRIM effects dimensionality reduction, and enables efficient computations, without any training data or additional information. Numerical tests on real-network time-varying edge flows demonstrate noticeable improvements of MultiL-KRIM over several state-of-the-art schemes. |
| title | Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2409.05135 |