Summary of Imputation Of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning, By Duc Thien Nguyen et al.
Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
by Duc Thien Nguyen, Konstantinos Slavakis, Dimitris Pados
First submitted to arxiv on: 8 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Signal Processing (eess.SP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper extends the framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. By incorporating graph topology through simplicial-complex arguments and Hodge Laplacians, MultiL-KRIM identifies latent geometries within features modeled as a point-cloud around a smooth manifold embedded in a reproducing kernel Hilbert space (RKHS). The paper uses linear approximating patches to add collaborative-filtering flavor to point-cloud approximations. Combining this with matrix factorizations enables dimensionality reduction and efficient computations without requiring training data or additional information. Numerical tests demonstrate improvements over state-of-the-art schemes on real-network time-varying edge flows. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a new way to fill in missing information in graphs that change over time. The method, called MultiL-KRIM, uses math ideas like manifolds and kernel spaces to find patterns in the data. It can help predict what might happen next by using information from similar past events. The authors tested their method on real-world graph data and found it works better than other methods they tried. |
Keywords
» Artificial intelligence » Dimensionality reduction » Manifold learning » Regression
