Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning

• URL: http://arxiv.org/abs/2409.05135v1
• Date: Sun, 8 Sep 2024 15:38:31 GMT
• Title: Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
• Authors: Duc Thien Nguyen, Konstantinos Slavakis, Dimitris Pados,
• Abstract 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. MultiL-KRIM uses simplicial-complex arguments and Hodge Laplacians to incorporate the graph topology. It exploits manifold-learning arguments to identify latent geometries within features which are modeled as a point-cloud around a smooth manifold embedded in a kernel reproducing Hilbert space (RKHS)
• Score: 4.129225533930965
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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