Graph Convolutional Networks (GCN) have been recently employed as core component in the construction of recommender system algorithms, interpreting user-item interactions as the edges of a bipartite graph. However, in the absence of side information, the majority of existing models adopt an approach of randomly initialising the user embeddings and optimising them throughout the training process. This strategy makes these algorithms inherently transductive, curtailing their ability to generate predictions for users that were unseen at training time. To address this issue, we propose a convolution-based algorithm, which is inductive from the user perspective, while at the same time, depending only on implicit user-item interaction data. We propose the construction of an item-item graph through a weighted projection of the bipartite interaction network and to employ convolution to inject higher order associations into item embeddings, while constructing user representations as weighted sums of the items with which they have interacted. Despite not training individual embeddings for each user our approach achieves state of-the-art recommendation performance with respect to transductive baselines on four real-world datasets, showing at the same time robust inductive performance.
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