Reference set thinning for the k-nearest neighbor decision rule
Bibliographic record
Abstract
The k-nearest neighbor decision rule (or k-NNR) is used to classify a point in d-space according to the dominant class among its k nearest neighbors in some reference set (in which each point has a known class). It is useful to find a small subset S' of S that can be used as the reference set instead. If the k-NNR always makes the same decision using either S or S' as the reference set, then S' is called an exact thinning of S for the k-NNR. We show that such an exact thinning can be determined easily from the k-Delaunay graph of S (which is dual to the order-k Voronoi diagram of S). This graph "encodes" a particular subset of S that must be included within any exact thinning for the k-NNR, and it also provides information on how this subset can be augmented into an exact thinning (although perhaps not a minimum one). In addition, we investigate how the k-Gabriel graph (which is a subgraph of the k-Delaunay graph) can be used to derive an inexact thinning of S that performs well in practice for the k-NNR. It is advantageous to use the k-Gabriel graph instead of the k-Delaunay graph, because the k-Gabriel graph is smaller and much easier to compute from the point set S.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".