Graph Model for NB model

User-Item graphs

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Neighborhood definition

Random Walks

Personalized PageRank or the SimRank method to determine the k most similar users.

Katz Measure

$$Katz(i,j)=\sum^\infty_{t=1}\beta^t \cdot \eta^{(t)}_{ij}$$

$\eta^{(t)}_{ij}$ is the number of walks of length $t$ between nodes $i$ and $j$. The value of $\beta$ is a discount factor.

$$K=\sum^\infty_{i=1}(\beta A)^i=(I-\beta A)^{-1}-I$$

User-User Graphs

Item-Item Graphs