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Abstract:
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We introduce a novel algorithm to study networks using multiscale analysis. The algorithm is based on an adaptive notion of a (unbalanced) Haar wavelet decomposition for the network adjacency matrix. The resulting transformation of the adjacency matrix yields a certain tree-based hierarchical agglomeration of nodes. We focus on the exact decompositions of the network, the corresponding approximation theory, and the network topology, particularly from the perspective of compression and fusion of the networks. We study the theoretical properties and present numerical simulations and discuss potential applications of the algorithm in network denoising, graph coarsening and community detection.
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