Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion

• URL: http://arxiv.org/abs/2010.00359v3
• Date: Thu, 20 May 2021 03:18:17 GMT
• Title: Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion
• Authors: Chenjian Pan and Chen Ling and Hongjin He and Liqun Qi and Yanwei Xu
• Abstract summary: We introduce a unified low-rank and sparse enhanced Tucker decomposition model for tensor completion. Our model possesses a sparse regularization term to promote a sparse core tensor, which is beneficial for tensor data compression. It is remarkable that our model is able to deal with different types of real-world data sets, since it exploits the potential periodicity and inherent correlation properties appeared in tensors.
• Score: 3.498620439731324
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due to the multidimensional nature of high-order tensors, the matrix approaches, e.g., matrix factorization and direct matricization of tensors, are often not ideal for tensor completion and recovery. In this paper, we introduce a unified low-rank and sparse enhanced Tucker decomposition model for tensor completion. Our model possesses a sparse regularization term to promote a sparse core tensor of the Tucker decomposition, which is beneficial for tensor data compression. Moreover, we enforce low-rank regularization terms on factor matrices of the Tucker decomposition for inducing the low-rankness of the tensor with a cheap computational cost. Numerically, we propose a customized ADMM with enough easy subproblems to solve the underlying model. It is remarkable that our model is able to deal with different types of real-world data sets, since it exploits the potential periodicity and inherent correlation properties appeared in tensors. A series of computational experiments on real-world data sets, including internet traffic data sets, color images, and face recognition, demonstrate that our model performs better than many existing state-of-the-art matricization and tensorization approaches in terms of achieving higher recovery accuracy.

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