View article

Online Tensor Factorization (OTF) is a fundamental tool in learning low-dimensional interpretable features from streaming multi-modal data. While various algorithmic and theoretical aspects of OTF have been investigated recently, general convergence guarantee to stationary points of the objective function without any incoherence or sparsity assumptions is still lacking even for the iid case. In this work, we introduce a novel OTF algorithm that learns a CANDECOMP/PARAFAC (CP) basis from a given stream of tensor-valued data under general constraints, including nonnegativity constraints that induce interpretability of learned CP basis. We prove that our algorithm converges almost surely to the set of stationary points of the objective function under the hypothesis that the sequence of data tensors is generated by some underlying Markov chain. Our setting covers the classical iid case as well as a wide range of …