  Inductive one-bit matrix completion is motivated by modern applications such
as recommender systems, where new users would appear at test stage with the
ratings consisting of only ones and no zeros. We propose a unified graph signal
sampling framework which enjoys the benefits of graph signal analysis and
processing. The key idea is to transform each user's ratings on the items to a
function (signal) on the vertices of an item-item graph, then learn structural
graph properties to recover the function from its values on certain vertices --
the problem of graph signal sampling. We propose a class of regularization
functionals that takes into account discrete random label noise in the graph
vertex domain, then develop the GS-IMC approach which biases the reconstruction
towards functions that vary little between adjacent vertices for noise
reduction. Theoretical result shows that accurate reconstructions can be
achieved under mild conditions. For the online setting, we develop a Bayesian
extension, i.e., BGS-IMC which considers continuous random Gaussian noise in
the graph Fourier domain and builds upon a prediction-correction update
algorithm to obtain the unbiased and minimum-variance reconstruction. Both
GS-IMC and BGS-IMC have closed-form solutions and thus are highly scalable in
large data. Experiments show that our methods achieve state-of-the-art
performance on public benchmarks.
