Preconditioned Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Completion
Authors: Yuanwei Zhang, Fengmiao Bian, Xiaoqun Zhang, Jian-Feng Cai
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical results highlight the efficiency of PRGD, outperforming state-of-the-art methods on both synthetic data and real-world video inpainting tasks. Code is available at https://github.com/Jiushanqing0418/PRGD-Tucker. 5. Numerical Experiments In this section, we proposed several numerical comparisons of our proposed PRGD algorithm with state-of-the-art algorithms that include RGD (Cai et al., 2020; Wang et al., 2023), for demonstrating the effectiveness of precondition, and Scaled GD (Tong et al., 2022), for comparisons with factorization based algorithms. |
| Researcher Affiliation | Academia | 1School of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China. 2Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China. 3Shanghai Artificial Intelligence Laboratory, Shanghai, China. Correspondence to: Jian-Feng Cai <EMAIL>, Xiaoqun Zhang <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Preconditioned RGD... Algorithm 2 Spectral Initialization with Trimming |
| Open Source Code | Yes | Code is available at https://github.com/Jiushanqing0418/PRGD-Tucker. |
| Open Datasets | Yes | We evaluate the performance of our proposed algorithm on the Tomato video from (Liu et al., 2012), as well as the Akiyo and Hall Monitor videos from the YUV video dataset1. 1http://trace.eas.asu.edu/yuv/ |
| Dataset Splits | No | The paper describes reconstructing a tensor from partially observed entries. While a sampling ratio of '10% of the pixels are observed' is mentioned for video inpainting, this refers to the observation mask for the completion problem, not a conventional training/validation/test split for a predictive model. |
| Hardware Specification | Yes | All simulations are performed in MATLAB r2023b with a 2.6GHZ Intel Xeon ICX Platinum 8358 CPU. |
| Software Dependencies | Yes | All simulations are performed in MATLAB r2023b with a 2.6GHZ Intel Xeon ICX Platinum 8358 CPU. |
| Experiment Setup | Yes | For our PRGD algorithm, we keep the hyperparamter ϵt a constant chosen from {10 3, 5 10 4, 10 4, 5 10 5}. Since no step size strategy is proposed for the Scaled GD algorithm in (Tong et al., 2022), to make a fair comparison, we tune the optimal constant step size for all tested algorithms and report the results. All simulations are performed in MATLAB r2023b with a 2.6GHZ Intel Xeon ICX Platinum 8358 CPU. ... We count the iteration numbers and runtimes of the tested algorithm until the relative error is less than 10 4. For each parameter setting, we perform five random trials and report the average results in Figure 2 and Figure 3. |