Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal

arXiv:2311.14427v2 Announce Type: replace-cross
Abstract: The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis. Recently, the Hodge Laplacian has come into focus as a generalisation of the ordinary Laplacian for higher-order graph models such as simplicial and cellular complexes. Akin to the traditional analysis of graph Laplacians, many authors analyse the smallest eigenvalues of the Hodge Laplacian, which are …

abstract analysis applications arxiv classification clustering cs.lg focus graph information machine machine learning math.at processing signal small the graph theory type