  Joint analysis of data from multiple information repositories facilitates
uncovering the underlying structure in heterogeneous datasets. Single and
coupled matrix-tensor factorization (CMTF) has been widely used in this context
for imputation-based recommendation from ratings, social network, and other
user-item data. When this side information is in the form of item-item
correlation matrices or graphs, existing CMTF algorithms may fall short.
Alleviating current limitations, we introduce a novel model coined coupled
graph-tensor factorization (CGTF) that judiciously accounts for graph-related
side information. The CGTF model has the potential to overcome practical
challenges, such as missing slabs from the tensor and/or missing rows/columns
from the correlation matrices. A novel alternating direction method of
multipliers (ADMM) is also developed that recovers the nonnegative factors of
CGTF. Our algorithm enjoys closed-form updates that result in reduced
computational complexity and allow for convergence claims. A novel direction is
further explored by employing the interpretable factors to detect graph
communities having the tensor as side information. The resulting community
detection approach is successful even when some links in the graphs are
missing. Results with real data sets corroborate the merits of the proposed
methods relative to state-of-the-art competing factorization techniques in
providing recommendations and detecting communities.
