Smooth and Sparse Regularization for NMF Hyperspectral Unmixing
Bibliographic record
Abstract
In this paper, we propose a matrix factorization method for hyperspectral unmixing using the linear mixing model. In this method, we add the arctan functions of the endmembers to the ℓ2-norm of the error in order to exploit the sparse property of the fractional abundances. Most of the energy of spectral signatures of materials is concentrated around the first few subbands resulting in smooth spectral signatures. To exploit this smoothness, we also add a weighted norm of the spectral signatures of the materials and to limit their nonsmooth errors. We propose a multiplicative iterative algorithm to solve this minimization problem as a nonnegative matrix factorization (NMF) problem. We apply our proposed Arctan-NMF method on the synthetic data from real spectral library and compare the performance of Arctan-NMF method with several state-of-the-art unmixing methods. Moreover, we evaluate the efficiency of Arctan-NMF on two different types of real hyperspectral data. Our simulations show that the Arctan-NMF is more effective than the state-of-the-art methods in terms of spectral angle distance and abundance angle distance.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".