Simultaneous Tensor Decomposition and Completion Using Factor Priors

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 36; no. 3; pp. 577 - 591
• Main Authors: Yi-Lei Chen, Chiou-Ting Hsu, Liao, Hong-Yuan Mark
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.03.2014; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation methods; Artificial intelligence; Brain modeling; Computer science; control theory; systems; Connectionism. Neural networks; Convergence; Decomposition; Effectiveness; Equations; Exact sciences and technology; factor priors; Factorization; Mathematical analysis; Mathematical model; Mathematical models; Matrix decomposition; multilinear model analysis; Pattern recognition. Digital image processing. Computational geometry; Tasks; Tensile stress; Tensor completion; Tensors; Tucker decomposition; Visualization; Computer vision; Data analysis; Adaptive resonance theory; Minimization; Modeling; multilinear model analysis; Missing data; Tensor completion; Completeness; Factorization method; factor priors; Tucker decomposition; Tensor method; Synthetic data
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2013.164

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.