Efficient Mining and Exploration of Multiple Axis-Aligned Intersecting Objects
Bibliographic record
Abstract
Identifying and quantifying the size of multiple intersections among a large number of axis-aligned geometric objects is an essential computational geometry problem. The ability to solve this problem can effectively inform a number of spatial data mining methods and can provide support in decision making for a variety of applications. Currently, the state-of-the-art approach for addressing such intersection problems resorts to an algorithmic paradigm, collectively known as the sweep-line algorithm. However, its application on specific instances of the problem inherits a number of limitations. With that mind, we design and implement a novel, exact, fast and scalable yet versatile, sweep-line based algorithm, named SLIG. Our algorithm can be employed in a number of problems and applications involving the efficient computation of numerous axis-aligned object intersection problems in multiple dimensions. The key idea of our algorithm lies in constructing an auxiliary data structure when the sweep line algorithm is applied, an intersection graph. This graph can effectively be used to provide connectivity properties among overlapping objects, as well as to inform the much harder problem of finding the location and size of the common area defined by multiple overlapping objects. A thorough experimental evaluation on synthetic data of various characteristics and sizes, demonstrates that SLIG performs significantly faster than classic sweep-line based algorithms. SLIG is not only faster and more versatile, but also provides a suite of powerful querying capabilities. To support the reproducibility of our methods, we make source code and datasets available.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.009 | 0.009 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".