t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions

Graph signal processing (GSP) techniques are powerful tools that model complex relationships within large datasets, being now used in a myriad of applications different areas including data science, communication networks, epidemiology, and sociology. Simple graphs can only pairwise among which prevents their application modeling networks with higher-order relationships. For this reason, some efforts have been made to generalize well-known graph more such as hypergraphs, allow capturing data. In paper, we provide new hypergraph framework (t-HGSP) based on novel tensor-tensor product algebra has emerged tool for preserving the intrinsic structures tensors. The proposed allows generalization traditional GSP while keeping dimensionality characteristic systems represented by hypergraphs. To end, core elements t-HGSP introduced, shifting operators signal. Fourier space is also defined, followed concept bandlimited signals sampling. our experiments, demonstrate benefits approach clustering denoising.