  To enhance the performance of the recommender system, side information is
extensively explored with various features (e.g., visual features and textual
features). However, there are some demerits of side information: (1) the extra
data is not always available in all recommendation tasks; (2) it is only for
items, there is seldom high-level feature describing users. To address these
gaps, we introduce the spectral features extracted from two hypergraph
structures of the purchase records. Spectral features describe the
\textit{similarity} of users/items in the graph space, which is critical for
recommendation. We leverage spectral features to model the users' preference
and items' properties by incorporating them into a Matrix Factorization (MF)
model. In addition to modeling, we also use spectral features to optimize.
Bayesian Personalized Ranking (BPR) is extensively leveraged to optimize models
in implicit feedback data. However, in BPR, all missing values are regarded as
negative samples equally while many of them are indeed unseen positive ones. We
enrich the positive samples by calculating the similarity among users/items by
the spectral features. The key ideas are: (1) similar users shall have similar
preference on the same item; (2) a user shall have similar perception on
similar items. Extensive experiments on two real-world datasets demonstrate the
usefulness of the spectral features and the effectiveness of our
spectrum-enhanced pairwise optimization. Our models outperform several
state-of-the-art models significantly.
