  Heterogeneous information networks (HINs) with rich semantics are ubiquitous
in real-world applications. For a given HIN, many reasonable clustering results
with distinct semantic meaning can simultaneously exist. User-guided clustering
is hence of great practical value for HINs where users provide labels to a
small portion of nodes. To cater to a broad spectrum of user guidance evidenced
by different expected clustering results, carefully exploiting the signals
residing in the data is potentially useful. Meanwhile, as one type of complex
networks, HINs often encapsulate higher-order interactions that reflect the
interlocked nature among nodes and edges. Network motifs, sometimes referred to
as meta-graphs, have been used as tools to capture such higher-order
interactions and reveal the many different semantics. We therefore approach the
problem of user-guided clustering in HINs with network motifs. In this process,
we identify the utility and importance of directly modeling higher-order
interactions without collapsing them to pairwise interactions. To achieve this,
we comprehensively transcribe the higher-order interaction signals to a series
of tensors via motifs and propose the MoCHIN model based on joint non-negative
tensor factorization. This approach applies to arbitrarily many, arbitrary
forms of HIN motifs. An inference algorithm with speed-up methods is also
proposed to tackle the challenge that tensor size grows exponentially as the
number of nodes in a motif increases. We validate the effectiveness of the
proposed method on two real-world datasets and three tasks, and MoCHIN
outperforms all baselines in three evaluation tasks under three different
metrics. Additional experiments demonstrated the utility of motifs and the
benefit of directly modeling higher-order information especially when user
guidance is limited.
