An Adaptive Approach to Learn Overcomplete Dictionaries With Efficient Numbers of Elements
Bibliographic record
Abstract
Dictionary learning for sparse representation has recently attracted attention among the signal processing society in a variety of applications such as denoising, classification, and compression. The number of elements in a learned dictionary is crucial since it governs specificity and optimality of sparse representation. Sparsity level, number of dictionary elements, and representation error are three correlated factors in which setting each pair of them results in a specific value of the third factor. An arbitrary selection of the number of dictionary elements affects either the sparsity level or/and the representation error. Despite recent advancements in training dictionaries, the number of dictionary elements is still heuristically set. To avoid the representation’s suboptimality, a systematic approach to adapt the elements’ number based on input datasets is essential. Some existing methods try to address this requirement such as enhanced K-SVD, sub-clustering K-SVD, and stage-wise K-SVD. However, it is not specified under which sparsity level and representation error criteria their learned dictionaries are size-optimized. We propose a new dictionary learning approach that automatically learns a dictionary with an efficient number of elements that provides both desired representation error and desired average sparsity level. In our proposed method, for any given representation error and average sparsity level, the number of elements in the learned dictionary varies based on content complexity of training datasets. The performance of the proposed method is demonstrated in image denoising. The proposed method is compared to state-of-the-art, and results confirm the superiority of the proposed approach.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".