Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
arXiv:1807.01589
Abstract
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high compressibility and flexibility of recently proposed tensor ring (TR) decomposition, we propose a new tensor completion approach named tensor ring weighted optimization (TR-WOPT). It finds the latent factors of the incomplete tensor by gradient descent algorithm, then the latent factors are employed to predict the missing entries of the tensor. We conduct various tensor completion experiments on synthetic data and real-world data. The simulation results show that TR-WOPT performs well in various high-dimension tensors. Furthermore, image completion results show that our proposed algorithm outperforms the state-of-the-art algorithms in many situations. Especially when the missing rate of the test images is high (e.g., over 0.9), the performance of our TR-WOPT is significantly better than the compared algorithms.
APSIPA2018 conference paper. arXiv admin note: substantial text overlap with arXiv:1805.08468
References in corpus (3)
Cited by in corpus (8)
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- Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion
- High-dimension Tensor Completion via Gradient-based Optimization Under Tensor-train Format
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- Low-rank Tensor Grid for Image Completion
- Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors
- Multi-Tensor Network Representation for High-Order Tensor Completion
- An Efficient Tensor Completion Method via New Latent Nuclear Norm