  The problem of basket recommendation~(BR) is to recommend a ranking list of
items to the current basket. Existing methods solve this problem by assuming
the items within the same basket are correlated by one semantic relation, thus
optimizing the item embeddings. However, this assumption breaks when there
exist multiple intents within a basket. For example, assuming a basket contains
\{\textit{bread, cereal, yogurt, soap, detergent}\} where \{\textit{bread,
cereal, yogurt}\} are correlated through the "breakfast" intent, while
\{\textit{soap, detergent}\} are of "cleaning" intent, ignoring multiple
relations among the items spoils the ability of the model to learn the
embeddings. To resolve this issue, it is required to discover the intents
within the basket. However, retrieving a multi-intent pattern is rather
challenging, as intents are latent within the basket. Additionally, intents
within the basket may also be correlated. Moreover, discovering a multi-intent
pattern requires modeling high-order interactions, as the intents across
different baskets are also correlated. To this end, we propose a new framework
named as \textbf{M}ulti-\textbf{I}ntent \textbf{T}ranslation \textbf{G}raph
\textbf{N}eural \textbf{N}etwork~({\textbf{MITGNN}}). MITGNN models $T$ intents
as tail entities translated from one corresponding basket embedding via $T$
relation vectors. The relation vectors are learned through multi-head
aggregators to handle user and item information. Additionally, MITGNN
propagates multiple intents across our defined basket graph to learn the
embeddings of users and items by aggregating neighbors. Extensive experiments
on two real-world datasets prove the effectiveness of our proposed model on
both transductive and inductive BR. The code is available online at
https://github.com/JimLiu96/MITGNN.
