[keywords]: recommender systems, link prediction, bipartite, graph auto-encoder framework, collaborative filtering

[1. Introduction]

Two main branches of recommender algorithms:

• content-based recommender systems: use content information of users and items to predict the next purchase of a user or rating of an item.
• collaborative filtering models: solve the matrix completion by collective interaction data.

[2. Matrix completion as link prediction on bipartite graphs]

• Rating matrix
• : number of users, : number of items
• either an observed rating or 0 (unobserved)
• : undirected bipartite user-item interaction graph
  ()

[2.1 Graph auto-encoders]

1. A graph encoder model
2. A pairwise decoder model

• : feature matrix
• adjacency matrix of a graph
• : node embedding matrix (: embedding size)
• 
• : users embedding matrix
• : items embedding matrix
• : a reconstructed rating matrix

Training: train the graph auto-encoder by minimizing the reconstruction error between the predicted ratings in and the observed ground-truth ratings in . (e.g. root mean square error, cross entropy)

[2.2 Graph convolutional encoder]

Idea: graph convolutional layer performs local operations that only take the first-order neighborhood of a node into account (can be seen as a form of message passing).

(a graph convolutional layer)
(a dense layer)

• : edge-type sepcific messages from items to user
• : either be (left normalization) or (symmetric normalization)
• : edge-type specific parameter matrix
• : initial feature vector of node
• accum(): an accumulation operation (e.g. stack(), sum())
• : an element-wise activation function (e.g. ReLU)
• : final embedding of user node

Combining side information with interaction data can alleviate performance bottlenecks related to the cold start problem.

Reference

1. Variantional graph auto-encoders
   Github Implementation