Tensor Wheel Decomposition and Its Tensor Completion Application
Authors: Zhong-Cheng Wu, Ting-Zhu Huang, Liang-Jian Deng, Hong-Xia Dou, Deyu Meng
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results elaborate that the proposed method is significantly superior to other tensor decomposition-based state-of-the-art methods on synthetic and real-world data, implying the merits of TW decomposition.In this section, we design substantial numerical experiments on synthetic and real-world data to verify the superiority of the proposed TW-TC method compared with others, which are constructed based on several commonly used tensor decompositions. |
| Researcher Affiliation | Academia | 1School of Mathematical Sciences, University of Electronic Science and Technology of China 2School of Science, Xihua University 3School of Mathematics and Statistics, Xi an Jiaotong University 4Pazhou Laboratory (Huangpu) |
| Pseudocode | Yes | Algorithm 1 The Alternating Least Squares Algorithm for TW Decomposition (TW-ALS).Algorithm 2 The Proximal Alternating Minimization (PAM)-Based Solver for TW-TC Model. |
| Open Source Code | Yes | The code is available at: https://github.com/zhongchengwu/code_TWDec. |
| Open Datasets | Yes | MSI Data. The tested MSI data sizes 200 200 31 (i.e., height width spectral), called Toy, which is cropped from the CAVE dataset2. 2https://www.cs.columbia.edu/CAVE/databases/multispectral/ Video Data. The tested video data contains two color videos3 (CVs): News and Container, and one hyperspectral video4 (HSV) [20]. 3http://trace.eas.asu.edu/yuv/ 4https://openremotesensing.net/knowledgebase/ |
| Dataset Splits | No | Subsequently, the partially observed tensors are generated by random sampling with two sampling rates (SRs): 20%, 40%. Afterwards, the partially observed tensors are created by random sampling with three SRs: 5%, 10%, 20%. These describe how missing data is simulated for the tensor completion task, not traditional train/validation/test splits of a dataset. |
| Hardware Specification | Yes | All the experiments are implemented in MATLAB (R2021a) on a computer of 64Gb RAM and Intel(R) Core(TM) i9-10900KF CPU: @3.70 GHz. |
| Software Dependencies | Yes | All the experiments are implemented in MATLAB (R2021a)... |
| Experiment Setup | Yes | More specifically, the synthetic data consists of 64 third-order, 81 fourth-order, and 32 fifth-order tensors, whose sizes are {I1 I2 I3 : I1, I2, I3 {45, 50, 55, 60}}, {I1 I2 I3 I4 : I1, I2, I3, I4 {18, 20, 22}}, and {I1 I2 I3 I4 I5 : I1, I2, I3, I4, I5 {7, 8}}, and Tucker-ranks are (6, 6, 6), (5, 5, 5, 5), and (3, 3, 3, 3, 3), respectively. All synthetic data are numerically renormalized into [0, 1]. Subsequently, the partially observed tensors are generated by random sampling with two sampling rates (SRs): 20%, 40%. Regarding TW-ranks, we empirically assign R1 = L3 and R3 = L1 = L2 based on observations of multiple third-order real-world data experiments, and then select ranks R1, R2 and R3 from the candidate sets {3, 4, 5}, {10, 15, 20, 25} and {2, 3}, respectively. |