Normalized Learning

Let $d_{u_{i}}$ denote the degree of the user $u_{i}$,and $d_{t_{p}}$ represent the degree of tag $t_{p}$ in a user-tag network. their cosine similarity can be rewritten as: $S_{e}\left(e,{e}'\right)={\frac {d_{t_{p}}d_{t_{q}}\delta \left(u_{i},u_{j}\right)+d_{u_{i}}d_{u_{j}}\delta \left(t_{p},t_{q}\right)}{{\sqrt {d_{u_{i}}^{2}+d_{t_{p}}^{2}}}{\sqrt {d_{u_{j}}^{2}+d_{t_{q}}^{2}}}}}$