Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
<|reference_start|>Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning: 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.<|reference_end|>
@article{nguyen2024imputation,
    title={Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel
  Regression and Manifold Learning},
    author={Duc Thien Nguyen, Konstantinos Slavakis, Dimitris Pados},
    journal={arXiv preprint arXiv:2409.05135},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05135},
    primaryClass={cs.LG eess.SP}
}