Journal
CIKM'17: PROCEEDINGS OF THE 2017 ACM CONFERENCE ON INFORMATION AND KNOWLEDGE MANAGEMENT
Volume -, Issue -, Pages 949-958Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3132847.3132945
Keywords
Tensor Rank Estimation; CP-based Tensor Nuclear Norm; CP Decomposition; Tensor Completion
Funding
- NSFC [61672444, 61272366]
- HKBU Faculty Research [FRG2/16-17/051]
- HKBU KTO grant [MPCF-004-2017/18]
- SZSTI [JCYJ20160531194006833]
- Hong Kong PhD Fellowship Scheme
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Tensor completion (TC) is a challenging problem of recovering missing entries of a tensor from its partial observation. One main TC approach is based on CP/Tucker decomposition. However, this approach often requires the determination of a tensor rank a priori. This rank estimation problem is difficult in practice. Several Bayesian solutions have been proposed but they often under/overestimate the tensor rank while being quite slow. To address this problem of rank estimation with missing entries, we view the weight vector of the orthogonal CP decomposition of a tensor to be analogous to the vector of singular values of a matrix. Subsequently, we define a new CP-based tensor nuclear norm as the Li-norm of this weight vector. We then propose Tensor Rank Estimation based on Li-regularized orthogonal CP decomposition (TREL1) for both CP-rank and Tucker-rank. Specifically, we incorporate a regularization with CP-based tensor nuclear norm when minimizing the reconstruction error in TC to automatically determine the rank of an incomplete tensor. Experimental results on both synthetic and real data show that: 1) Given sufficient observed entries, TREL1 can estimate the true rank (both CP-rank and Tucker-rank) of incomplete tensors well; 2) The rank estimated by TREL1 can consistently improve recovery accuracy of decomposition-based TC methods; 3) TREL1 is not sensitive to its parameters in general and more efficient than existing rank estimation methods.
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