Distributed Graph Learning with Smooth Data Priors

• URL: http://arxiv.org/abs/2112.05887v1
• Date: Sat, 11 Dec 2021 00:52:02 GMT
• Title: Distributed Graph Learning with Smooth Data Priors
• Authors: Isabela Cunha Maia Nobre, Mireille El Gheche, Pascal Frossard
• Abstract summary: We propose a novel distributed graph learning algorithm, which permits to infer a graph from signal observations on the nodes. Our results show that the distributed approach has a lower communication cost than a centralised algorithm without compromising the accuracy in the inferred graph.
• Score: 61.405131495287755
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely the data that lives on the graph nodes. However, there are settings where data cannot be collected easily or only with a non-negligible communication cost. In such cases, distributed processing appears as a natural solution, where the data stays mostly local and all processing is performed among neighbours nodes on the communication graph. We propose here a novel distributed graph learning algorithm, which permits to infer a graph from signal observations on the nodes under the assumption that the data is smooth on the target graph. We solve a distributed optimization problem with local projection constraints to infer a valid graph while limiting the communication costs. Our results show that the distributed approach has a lower communication cost than a centralised algorithm without compromising the accuracy in the inferred graph. It also scales better in communication costs with the increase of the network size, especially for sparse networks.

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