graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, ...
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graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the approximation space is not available analytically and must be computed. We propose perturbations of Lagrange bases on graphs, where the Lagrange functions come from a class of functions analogous to classical splines. The basisfunctions we consider have local support, with each basis function obtained by solving a small energy minimization problem related to a differential operator on the graph. We present B infinity error estimates between the local basis and the corresponding interpolatory Lagrange basisfunctions in cases where the underlying graph satisfies an assumption on the connections of vertices where the function is not known, and the theoretical bounds are examined further in numerical experiments. Included in our analysis is a mixed-norm inequality for positive definite matrices that is tighter than the general estimate ||Al||(infinity) <= root n ||A||(2). (c) 2024 Published by Elsevier Inc.
graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a ...
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graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based on the underlying graph structure, employing an algorithm that relies exclusively on centrality measures and modularity, without requiring the input of the number of subdomains. Subsequently, we integrate PUMs with a local graphbasis function (GBF) approximation method to develop cost-effective global interpolation schemes. We also discuss numerical experiments conducted on both synthetic and real datasets to assess the performance of this presented technique.
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