We consider the problem of low-rank decomposition of incomplete multiwaytensors. Since many real-world data lie on an intrinsically low dimensionalsubspace, tensor low-rank decomposition with missing entries has applicationsin many data analysis problems such as recommender systems and imageinpainting. In this paper, we focus on Tucker decomposition which represents anNth-order tensor in terms of N factor matrices and a core tensor viamultilinear operations. To exploit the underlying multilinear low-rankstructure in high-dimensional datasets, we propose a group-based log-sumpenalty functional to place structural sparsity over the core tensor, whichleads to a compact representation with smallest core tensor. The method forTucker decomposition is developed by iteratively minimizing a surrogatefunction that majorizes the original objective function, which results in aniterative reweighted process. In addition, to reduce the computationalcomplexity, an over-relaxed monotone fast iterative shrinkage-thresholdingtechnique is adapted and embedded in the iterative reweighted process. Theproposed method is able to determine the model complexity (i.e. multilinearrank) in an automatic way. Simulation results show that the proposed algorithmoffers competitive performance compared with other existing algorithms.
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