Paper notes: knowledge map kgat (unfinished temporary storage)

Abstract : Share your understanding of the paper . See the original X. Wang et al., KGAT: Knowledge Graph Attention Network for Recommendation, KDD 2019.

0. Contribution of thesis

• In the collaborative knowledge map (Collaborative knowledge graph) Modeling high-order relationships is shown in , Use project information for better recommendation system modeling .
• Propose a new method KGAT, Provide a high-order model under the framework of graph neural network .
• Fast and good .
• Provide code : https://github.com/xiangwang1223/knowledge_graph_attention_network.

1. Basic ideas

chart 1. user - project - Property example

user And user, user And item The relationship between has certain transitivity . The number of passes is the corresponding order (order). order = 3 when , $u_1$ And $i_3$ and $i_4$ Link ; order = 4 when , $u_1$ And $u_2,u_3$ Link .

2. Problem modeling

surface 1. The symbol table

Symbol	meaning	remarks
$\mathcal{U}$	User set
$\mathcal{I}$	Project collection
${\mathcal{G}}_1$	user - The second part of the project	${\mathcal{G}}_1\subseteq \mathcal{U}\times \mathcal{I}$, It can be considered as a directed graph
$\mathcal{E}$	Set of entities	It can be a user or a project
$\mathcal{R}$	Relational sets
${\mathcal{G}}_2$	Knowledge map	${\mathcal{G}}_2\subseteq \mathcal{E}\times \mathcal{R}\times \mathcal{E}$, It's a digraph
$\mathcal{A}$	Project entity alignment	$\mathcal{A}\subset \mathcal{I}\times \mathcal{E}$
$\mathcal{G}$	Unified knowledge map	$\mathcal{G}\subseteq {\mathcal{E}}^{\prime }\times {\mathcal{R}}^{\prime }\times {\mathcal{E}}^{\prime }$
${\mathcal{E}}^{\prime }$	All entities	${\mathcal{E}}^{\prime }=\mathcal{E}\cup \mathcal{U}$, Include users 、 project 、 Project properties
$-r$	The reverse of the relationship	The movie By Starring actors

• user - The second part of the project .
  $\{(u,y_{ui},i)|u\in \mathcal{U},i\in \mathcal{I}\}$, $y_{ui}=1$ Indicates that the user is associated with the project ( Watching the film 、 Bought goods ).
  Make complaints : People who engage in machine learning can write this model , Obviously, it is a common figure , No need at all $y_{ui}$.

• Project knowledge map
  $\{(h,r,t)|h,t\in \mathcal{E},r\in \mathcal{R})\}$.

• Project entity alignment
  $\mathcal{A}=\{(i,e)|i\in \mathcal{I},e\in \mathcal{E}\}$ Mistake . Actually $\mathcal{A}$ Is a subset of the latter .

• Problem description
  Input : Collaborative knowledge map $\mathcal{G}$;
  Output : ${\hat{y}}_{ui}$, The user $u$ And projects $i$ Related ( like , Want to buy ) The possibility of .

3. Method

The embedded (embedding) Learning a vector for each entity , Used to indicate it .
After embedding , You can use the distance between vectors to calculate the similarity of entities ( Relevance ).

4. doubt

• It is clearly a three part graph ( user 、 project 、 attribute ), Why do we have to make a bipartite picture of users and projects , And make items and attributes into a knowledge map ？