Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements
Authors: Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan
IJCAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conducts experiments to first verify the exact recovery guarantee in Theorem 4 for (3) from Gaussian measurements, then to verify the exact recovery guarantee in Theorem 6 for tensor completion (8). Both (3) and (8) can be solved by the standard ADMM [Lu et al., 2018b]. First, we test on random tensors, provided sufficient number of measurements as suggested in Theorem 4. We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables. We generate A Rm (n2n3) with its entries being i.i.d., zero-mean, 1 m-variance Gaussian variables. Then, let y = Avec(X 0). We choose n = 10, 20, 30, n3 = 5, r = 0.2n and r = 0.3n. We set the number of measurements m = 3r(2n r)n3 +1 as in Theorem 4. The results are given in Table 1, in which ˆX is the solution to (11). It can be seen that the relative errors ˆX X 0 F / X 0 F are very small and the tubal ranks of ˆX are correct. |
| Researcher Affiliation | Collaboration | Canyi Lu1, Jiashi Feng2, Zhouchen Lin3,4 Shuicheng Yan5,2 1 Department of Electrical and Computer Engineering, Carnegie Mellon University 2 Department of Electrical and Computer Engineering, National University of Singapore 3 Key Laboratory of Machine Perception (MOE), School of EECS, Peking University 4 Cooperative Medianet Innovation Center, Shanghai Jiao Tong University 5 360 AI Institute |
| Pseudocode | Yes | Algorithm 1 T-SVD Input: A Rn1 n2 n3. Output: T-SVD components U, S and V of A. |
| Open Source Code | Yes | The codes of our methods can be found at https://sites.google.com/site/canyilu/ |
| Open Datasets | No | The paper generates synthetic data for its experiments, for example: 'We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables.' It does not use publicly available datasets. |
| Dataset Splits | No | The paper focuses on theoretical recovery guarantees and their empirical verification using generated data, rather than on standard training/validation/test splits of a dataset. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., GPU models, CPU types, or cloud platforms) used for conducting the experiments. |
| Software Dependencies | No | The paper mentions 'Matlab command fft' and that the problems can be solved by 'standard ADMM [Lu et al., 2018b]', but it does not provide specific version numbers for MATLAB or any other software libraries or dependencies. |
| Experiment Setup | Yes | We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables. We generate A Rm (n2n3) with its entries being i.i.d., zero-mean, 1 m-variance Gaussian variables. Then, let y = Avec(X 0). We choose n = 10, 20, 30, n3 = 5, r = 0.2n and r = 0.3n. We set the number of measurements m = 3r(2n r)n3 +1 as in Theorem 4. |