Signal Processing on Simplicial Complexes with Vertex Signals
نویسندگان
چکیده
In classical graph signal processing (GSP), the underlying topological structures are restricted in terms of dimensionality. A or a 1-complex is combinatorial object that models binary relations, which do not directly capture complex high arity relations. One possible dimensional generalization graphs simplicial complex. this paper, we develop framework on complexes with vertex signals, recovers traditional GSP theory. We introduce concept generalized Laplacian, allows us to embed into and hence perform similar GSP. show Laplacian satisfies several desirable properties, same as Laplacian. propose method learn 2-complex demonstrate how by applying both synthetic real data. observe performance gains our experiments when 2-complexes used model data, compared approach restricting 1-complexes.
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ژورنال
عنوان ژورنال: IEEE Access
سال: 2022
ISSN: ['2169-3536']
DOI: https://doi.org/10.1109/access.2022.3167055