A new weighted ℓ<inf>p</inf>-norm for sparse hyperspectral unmixing
Bibliographic record
Abstract
In this paper, we propose a new approach to approximate the ℓ0-norm for the sparse hyperspectral unmixing. In our method, we first approximate the ℓ0-norm with the ℓp-norm and reduce p iteratively. It is motivated by our theorem that the set of minima for the ℓp-norm problem is continuous in terms of p, which implies that smooth iterative reduction of p results in an enhanced solution. We introduce a weighted ℓ1-norm approximation of the ℓp-norm problem involving a parameter e to deal with the fact that the ℓp-norm problem is not Lipschitz continuous for p < 1 and propose an updating rule for the pair (p, ∊). To solve this approximated problem using the previous solution, we employ the alternating direction method of multipliers (ADMM) approach to derive the remaining updating steps. Experimental results show that our proposed method outperforms several state-of-the-art methods in terms of the reconstruction errors and their probability of success.
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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 | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".