Maximal vector computation in large data sets
Bibliographic record
Abstract
Finding the maximals in a collection of vectors is relevant to many applications. The maximal set is related to the convex hull— and hence, linear optimization—and nearest neighbors. The maximal vector problem has resurfaced with the advent of skyline queries for relational databases and skyline algorithms that are external and relationally well behaved. The initial algorithms proposed for maximals are based on divide-and-conquer. These established good average and worst case asymptotic running times, showing it to be O(n) average-case, where n is the number of vectors. However, they are not amenable to externalizing. We prove their performance is quite bad with respect to the dimensionality, k, of the problem. We demonstrate that the more recent external skyline algorithms are actually better behaved, although they do not have as good an apparent asymptotic complexity. We introduce a new external algorithm, LESS, that combines the best features of these, experimentally evaluate its effectiveness and improvement over the field, and prove its average-case running time is O(kn). 1
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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 | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".