Pairwise Rayleigh quotient classifier with application to the analysis of breast tumors
Bibliographic record
Abstract
In this paper, we propose a new supervised learning method for binary classification, named the pairwise Rayleigh quotient (PRQ) classifier, in which the nonlinearity is achieved by employing kernel functions. The PRQ classifier generates a Rayleigh quotient based on a set of pairwise constraints, which consequently leads to a generalized eigenvalue problem with low complexity of implementation. The PRQ classifier is applied in the original feature space for linear classification, as well as in a transformed feature space by employing the triangle kernel for nonlinear classification, to discriminate malignant breast tumors from a set of 57 regions in mammograms, of which 20 are related to malignant tumors and 37 to benign masses. Nine different feature combinations are studied. Experimental results demonstrate that the proposed linear PRQ classifier provides results comparable to those obtained with Fisher linear discriminant analysis (FLDA). In the case of nonlinear classification, the PRQ classifier with the triangle kernel provides a perfect performance of 1.0 for all of the nine feature combinations evaluated in terms of the area under the receiver operating characteristics curve, but with good robustness limited to the setting of the kernel parameter in a certain range. We propose a measure of robustness to evaluate the PRQ classifier.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".