  Within-basket recommendation reduces the exploration time of users, where the
user's intention of the basket matters. The intent of a shopping basket can be
retrieved from both user-item collaborative filtering signals and multi-item
correlations. By defining a basket entity to represent the basket intent, we
can model this problem as a basket-item link prediction task in the
User-Basket-Item~(UBI) graph. Previous work solves the problem by leveraging
user-item interactions and item-item interactions simultaneously. However,
collectivity and heterogeneity characteristics are hardly investigated before.
Collectivity defines the semantics of each node which should be aggregated from
both directly and indirectly connected neighbors. Heterogeneity comes from
multi-type interactions as well as multi-type nodes in the UBI graph. To this
end, we propose a new framework named \textbf{BasConv}, which is based on the
graph convolutional neural network. Our BasConv model has three types of
aggregators specifically designed for three types of nodes. They collectively
learn node embeddings from both neighborhood and high-order context.
Additionally, the interactive layers in the aggregators can distinguish
different types of interactions. Extensive experiments on two real-world
datasets prove the effectiveness of BasConv. Our code is available online at
https://github.com/JimLiu96/basConv.
