Kernel Orthogonal Nonnegative Matrix Factorization: Application to Multispectral Document Image Decomposition
Bibliographic record
Abstract
As a nonlinear extension of the standard nonnegative matrix factorization (NMF), kernel-based variants have demonstrated to be more effective for discovering meaningful latent features from raw data. However, many existing kernel methods allow only obtaining the basis matrix in the projected feature space, which prevents its inverse mapping back to the original space as requested in many applications. In this work, we propose a new kernel orthogonal NMF method that does not suffer from the pre-image issue. We incorporate the orthogonality constraint as an optimization problem over the Stiefel manifold to improve the sparsity and the model’s clustering properties. We solve the proposed model with an efficient optimization approach based on the alternating direction method of multipliers (ADMM) scheme and the projected gradients method. We validate our model on the task of blind decomposition of real-world Multispectral (MS) document images. Our experiments demonstrate the competitiveness of our proposed model in comparison to the state-of-the-art techniques.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".