MetricMap: An Embedding Technique for Processing Distance-Based Queries in Metric Spaces
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Bibliographic record
Abstract
In this paper, we present an embedding technique, called MetricMap, which is capable of estimating distances in a pseudometric space. Given a database of objects and a distance function for the objects, which is a pseudometric, we map the objects to vectors in a pseudo-Euclidean space with a reasonably low dimension while preserving the distance between two objects approximately. Such an embedding technique can be used as an approximate oracle to process a broad class of distance-based queries. It is also adaptable to data mining applications such as data clustering and classification. We present the theory underlying MetricMap and conduct experiments to compare MetricMap with other methods including MVP-tree and M-tree in processing the distance-based queries. Experimental results on both protein and RNA data show the good performance and the superiority of MetricMap over the other methods.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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 it