Table 1 Notations and definitions in hypergraph learning model
Notation | Definition |
|---|---|
G=(V,E,ω) | Hypergraph of a face image set containing n images and m attributes. |
V={v1,v2,…,v n } | The set of vertices. |
E={e1,e2,…,e m } | The set of hyperedges. |
ω(e i ) | The weight of the hyperedge e i . \(\sum _{i=1}^{m} \omega (e_{i})=1\) and ω(e i )≥0. |
W | The diagonal matrix of the hyperedge weights. |
h(v i ,e i ) | The incidence between a pair of vertex v i and hyperedge e i . |
H | The incidence matrix of the hypergraph. |
δ(e i ) | The degree of the hyperedge e i . |
D e | The diagonal matrix of the hyperedge degrees. |
d(v i ) | The degree of the vertex v i . |
D v | The diagonal matrix of the vertex degrees. |
Y={Y i,j ,1≤i,j≤n} | The source similarity matrix. Y i,j represents the distance between image i and image j. y k denotes a column of Y. |
F={F i,j ,1≤i,j≤n} | The target similarity matrix. F i,j represents the reformed distance between image i and image j. f k denotes a column of F. |