Scalable and Explainable 1-Bit Matrix Completion via Graph Signal Learning

One-bit matrix completion is an important class of positive-unlabeled (PU) learning problems where the observations consist only positive examples, e.g., in top-N recommender systems. For first time, we show that 1-bit can be formulated as problem recovering clean graph signals from noise-corrupted hypergraphs. This makes it possible to enjoy recent advances signal learning. Then, propose spectral (SGMC) method, which recover underlying distributed systems by filtering noisy data frequency domain. Meanwhile, provide micro- and macro-level explanations following vertex-frequency analysis. To tackle computational memory issue performing operations on large graphs, construct a scalable Nystrom algorithm efficiently compute orthonormal eigenvectors. Furthermore, also develop polynomial sparse filters remedy accuracy loss caused approximations. We demonstrate effectiveness our algorithms recommendation tasks, results three large-scale real-world datasets SGMC outperform state-of-the-art while requiring small fraction training time compared baselines.