Web: http://arxiv.org/abs/2201.11720

Sept. 15, 2022, 1:11 a.m. | Maosheng Yang, Elvin Isufi, Michael T. Schaub, Geert Leus

cs.LG updates on arXiv.org arxiv.org

We study linear filters for processing signals supported on abstract
topological spaces modeled as simplicial complexes, which may be interpreted as
generalizations of graphs that account for nodes, edges, triangular faces etc.
To process such signals, we develop simplicial convolutional filters defined as
matrix polynomials of the lower and upper Hodge Laplacians. First, we study the
properties of these filters and show that they are linear and shift-invariant,
as well as permutation and orientation equivariant. These filters can also be …

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