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Simultaneous Tensor Decomposition and Completion Using Factor Priors
March 2014 (vol. 36 no. 3)
pp. 577-591
Yi-Lei Chen, National Tsing Hua University, Hsinchu
Chiou-Ting Hsu, National Tsing Hua University, Hsinchu
Hong-Yuan Mark Liao, Academia Sinica, Taipei and National Chiao Tung University, Hsinchu
The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.
Index Terms:
Tensile stress,Equations,Matrix decomposition,Mathematical model,Approximation methods,Visualization,Brain modeling,multilinear model analysis,Tensor completion,Tucker decomposition,factor priors
Citation:
Yi-Lei Chen, Chiou-Ting Hsu, Hong-Yuan Mark Liao, "Simultaneous Tensor Decomposition and Completion Using Factor Priors," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 3, pp. 577-591, March 2014, doi:10.1109/TPAMI.2013.164
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