A Learnable Group-Tube Transform Induced Tensor Nuclear Norm and Its Application for Tensor Completion
Bibliographic record
Abstract
The transform-based tensor nuclear norm (TNN) methods have shown good recovery results for tensor completion. However, the TNN methods are based on the single-tube transforms in which transforms are applied to each tube independently. The performance of the single-tube transform-based TNN methods is not good for recovery of missing tubes in multidimensional images (e.g., all the observations are missing in a pixel location of multispectral images). The main aim of this paper is to address this issue by proposing and developing a learnable group-tube transform-based TNN (GTNN) method that can effectively explore the correlation of neighboring tubes by leveraging a learnable group-tube transform. The proposed learnable group-tube transform is a separable three-dimensional transform that consists of a one-dimensional spectral/temporal transform (i.e., single-tube transform) and a two-dimensional spatial transform. Such group-tube transform can effectively explore the correlation of neighboring tubes. Based on the elaborately designed low-rank metric GTNN, we suggest a low-rank tensor completion model. To solve this highly nonconvex model, we design an efficient multiblock proximal alternating minimization algorithm and establish the convergence guarantee. A variety of numerical experiments on real-world multidimensional imaging data including traffic speed data, color images, videos, and multispectral images collectively manifest that the GTNN method outperforms some state-of-the-art TNN methods especially when the observations along tubes are missing.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".