Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
For practitioners dealing with incomplete high-dimensional data, this method offers improved recovery accuracy under extreme missing rates.
The paper proposes a tensor completion method (TR-WOPT) using tensor ring decomposition and gradient descent, achieving superior performance on high-dimension tensors and image completion, especially at missing rates over 0.9 where it significantly outperforms state-of-the-art algorithms.
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.