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In this article, we derive a Bayesian model to learning the sparse and lowrank PARAFAC decomposition for the observed tensor with missing values via theelastic net, with property to find the true rank and sparse factor matrix whichis robust to the noise. We formulate efficient block coordinate descentalgorithm and admax stochastic block coordinate descent algorithm to solve it,which can be used to solve the large scale problem. To choose the appropriaterank and sparsity in PARAFAC decomposition, we will give a solution path bygradually increasing the regularization to increase the sparsity and decreasethe rank. When we find the sparse structure of the factor matrix, we can fixedthe sparse structure, using a small to regularization to decreasing therecovery error, and one can choose the proper decomposition from the solutionpath with sufficient sparse factor matrix with low recovery error. We test thepower of our algorithm on the simulation data and real data, which show it ispowerful.

Learning the Sparse and Low Rank PARAFAC Decomposition via the Elastic Net