Table 1 Notation
Notation | Description |
|---|---|
\(H = ({{\mathcal {V}}}, {{\mathcal {E}}})\) | Static hypergraph with sets of hypernodes \({{\mathcal {V}}}\) and hyperedges \({{\mathcal {E}}}\) |
\(G = ({{\mathcal {V}}}, {{\mathcal {C}}})\) | Normal graph with sets of normal-nodes \({{\mathcal {V}}}\) and normal-edges \({{\mathcal {C}}}\) |
\(B = ({{\mathcal {V}}}, {{\mathcal {E}}}, {{\mathcal {R}}})\) | Bipartite graph with sets of bipartite-nodes \({{\mathcal {V}}},{{\mathcal {E}}}\) and bipartite-edges \({{\mathcal {R}}}\) |
\(N = |{{\mathcal {V}}}|\) | Number of hypernodes, number of normal-nodes |
\(M = |{{\mathcal {E}}}|\) | Number of hyperedges |
\(L = |{{\mathcal {R}}}|\) | Number of bipartite-edges |
\(K = |{{\mathcal {C}}}|\) | Number of normal-edges |
D | Number of dimensions of embedding vectors |
\({\textbf {X}} = [{\textbf {x}}_v]_{v \in {{\mathcal {V}}}}\) | Embedding vectors of hypernodes |
\({\textbf {Y}} = [{\textbf {y}}_e]_{e \in {{\mathcal {E}}}}\) | Embedding vectors of hyperedges |
\({\textbf {H}}\) | Incidence matrix of a hypergraph, adjacency matrix of a bipartite graph |
\({\tilde{\textbf{H}}}\) | Double-centered incidence matrices of a hypergraph |
\({\textbf {A}}\) | Adjacency matrix of a normal graph |
\({\textbf {I}}_N\) | \(N \times N\) identity matrix |
\({\textbf {J}}_N\) | \(N \times N\) centering matrix |
\({\textbf {1}}_N\) | N-dimensional vectors whose elements are all 1 |
\({{\mathcal {H}}}^{(T)}\) | Dynamic hypergraph, sequence of T static hypergraphs |
T | Number of hypergraph stnapshots |