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Joint analysis of data from multiple information repositories facilitatesuncovering the underlying structure in heterogeneous datasets. Single andcoupled matrix-tensor factorization (CMTF) has been widely used in this contextfor imputation-based recommendation from ratings, social network, and otheruser-item data. When this side information is in the form of item-itemcorrelation matrices or graphs, existing CMTF algorithms may fall short.Alleviating current limitations, we introduce a novel model coined coupledgraph-tensor factorization (CGTF) that judiciously accounts for graph-relatedside information. The CGTF model has the potential to overcome practicalchallenges, such as missing slabs from the tensor and/or missing rows/columnsfrom the correlation matrices. A novel alternating direction method ofmultipliers (ADMM) is also developed that recovers the nonnegative factors ofCGTF. Our algorithm enjoys closed-form updates that result in reducedcomputational complexity and allow for convergence claims. A novel direction isfurther explored by employing the interpretable factors to detect graphcommunities having the tensor as side information. The resulting communitydetection approach is successful even when some links in the graphs aremissing. Results with real data sets corroborate the merits of the proposedmethods relative to state-of-the-art competing factorization techniques inproviding recommendations and detecting communities.

Coupled Graphs and Tensor Factorization for Recommender Systems and Community Detection