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Statduck
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  • User-Item graphs
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  1. Recommender System
  2. Collaborative Filtering

Graph Model for NB model

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Last updated 3 years ago

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User-Item graphs

Neighborhood definition

Random Walks

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

Katz Measure

User-User Graphs

Item-Item Graphs

Katz(i,j)=βˆ‘t=1∞βtβ‹…Ξ·ij(t)Katz(i,j)=\sum^\infty_{t=1}\beta^t \cdot \eta^{(t)}_{ij}Katz(i,j)=t=1βˆ‘βˆžβ€‹Ξ²tβ‹…Ξ·ij(t)​

Ξ·ij(t)\eta^{(t)}_{ij}Ξ·ij(t)​ is the number of walks of length ttt between nodes iii and jjj. The value of Ξ²\betaΞ² is a discount factor.

K=βˆ‘i=1∞(Ξ²A)i=(Iβˆ’Ξ²A)βˆ’1βˆ’IK=\sum^\infty_{i=1}(\beta A)^i=(I-\beta A)^{-1}-IK=i=1βˆ‘βˆžβ€‹(Ξ²A)i=(Iβˆ’Ξ²A)βˆ’1βˆ’I
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