Correlational Learning

The singular value decomposition of user-tag network M is given by $M=U\Sigma V^{T}$, where columns of U and V are the left and right singular vectors and $\Sigma$ is the diagonal matrix whose elements are singular values.

${\vec {u}}_{i}({\vec {t}}_{1},{\vec {t}}_{2},...,{\vec {t}}_{m})=u_{i}(t_{1},t_{2},...t_{n})V$ So we can get $S_{e}\left(e,{e}'\right)=\alpha S_{u}\left(u_{i},u_{j}\right)+\left(1-\alpha \right)S_{t}\left(t_{p},t_{q}\right)$

where $S_{u}(u_{i},u_{j})={\frac {{\vec {u}}_{i}{\vec {u}}_{j}}{\left\|{\vec {u}}_{i}\right\|\left\|{\vec {u}}_{j}\right\|}}$ and $S_{t}(t_{i},t_{j})={\frac {{\vec {t}}_{i}{\vec {t}}_{j}}{\left\|{\vec {t}}_{i}\right\|\left\|{\vec {t}}_{j}\right\|}}$, Parameter α (0 ≤ α ≤ 1) controls the weights of users and tags. Considering the balance between user similarity and tag similarity, α is set to 0.5.