Spectral Clustering and Kernel PCA are Learning Eigenfunctions
Bibliographic record
Abstract
Dans cet article, on montre une équivalence directe entre la classification spectrale et l'ACP à noyau, et on montre que les deux sont des cas particuliers d'un problème plus général, celui d'apprendre les fonctions propres d'un noyau. Ces fonctions fournissent une base pour un espace de Hilbert dont le produit scalaire est défini par rapport à la densité des données. Les fonctions propres définissent une transformation de coordonnées naturelles pour de nouveaux points, alors que des méthodes comme la classification spectrale et les 'Laplacian eigenmaps' ne fournissaient un système de coordonnées que pour les exemples d'apprentissage. Cette analyse suggère aussi de nouvelles approches à l'apprentissage non-supervisé dans lesquelles on extrait des abstractions qui résument la densité des données, telles que des variétés et des classes naturelles.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".