Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 64, Issue 18, Pages 4817-4829Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2016.2572047
Keywords
Tucker decomposition; low rank tensor decomposition; tensor completion; iterative reweighted method
Categories
Funding
- National Science Foundation of China [61428103, 61522104]
- National Science Foundation [ECCS-1408182]
- Air Force Office of Scientific Research [FA9550-16-1-0243]
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We consider the problem of low-rank decomposition of incomplete tensors. Since many real-world data lie on an intrinsically low-dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data analysis problems such as recommender systems and image inpainting. In this paper, we focus on Tucker decomposition which represents an Nth-order tensor in terms of N factor matrices and a core tensor via multilinear operations. To exploit the underlying multilinear low-rank structure in high-dimensional datasets, we propose a group-based log-sum penalty functional to place structural sparsity over the core tensor, which leads to a compact representation with smallest core tensor. The proposed method is developed by iteratively minimizing a surrogate function that majorizes the original objective function. This iterative optimization leads to an iteratively reweighted least squares algorithm. In addition, to reduce the computational complexity, an over-relaxed monotone fast iterative shrinkage-thresholding technique is adapted and embedded in the iterative reweighted process. The proposed method is able to determine the model complexity (i.e., multilinear rank) in an automatic way. Simulation results show that the proposed algorithm offers competitive performance compared with other existing algorithms.
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