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I've been reading this paper on Knowledge Graph Reasoning for Explainable Recommendation lately, and I don't understand a particular section:

Specifically, the scoring function $f((r,e)|u)$ maps any edge $(r,e)$ to a real-valued score conditioned on user $u$. Then, the user-conditional pruned action space of state $s_t$ denoted by $A_t(u)$ is defined as:

$A_t(u) = \{(r,e)| rank(f((r,e)|u))) \leq \alpha ,(r,e) \in A_t\} $

where $\alpha$ is a predefined integer that upper bounds the size of the action space.

Details about the scoring function can be found in the attached paper - what I don't understand is - What does rank mean, here? Is the thing inside of it a matrix? It would be great if someone could explain the expression for the user conditional pruned action space in greater detail.

References:

  1. Reinforcement Knowledge Graph Reasoning for Explainable Recommendation [Yikun Xian, Zuohui Fu, S. Muthukrishnan, Gerard de Melo, Yongfeng Zhang]
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$\text{rank}(f((r,e)|u))$ in $A_t(u)$ means to compute the value of scoring function $f$ for all pairs $(r,e)\in A_t$ which are conditioned by $u$, then sort them in a descending order. The rank of the $f((r,e)|u)$ in this order is equal to $\text{rank}(f((r,e)|u))$. Hence $\text{rank}(f((r,e)|u)) \leqslant \alpha$ means to select the $\alpha$ top most scored pairs.

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  • $\begingroup$ $f$ is a function that maps $(r, e)$ to some real value. $f((r,e|u)$ is a scalar not a matrix . Rank of it is probably result based on some ranking system they use, not the matrix rank. $\endgroup$ – Brale Jun 2 at 13:26
  • $\begingroup$ @Brale You're right. It's updated. $\endgroup$ – OmG Jun 2 at 14:05

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