An Automated Displaced Proportional Circle Map Using Delaunay Triangulation and an Algorithm for Node Overlap Removal
Bibliographic record
Abstract
Proportional circle maps are a popular method for visualizing quantitative data on a map. Circles are scaled proportionally based on the data provided; larger circles represent larger quantities. The circles require two values, a location and a numeric quantity. For data that have a wide range of values, the resulting map will produce clutter and overlap in which large symbols obscure the information contained in smaller circles. Some previous solutions to this problem are modifying and improving the contrast between symbols, or using stacking algorithms so all symbols are visible. This article proposes the displaced proportional symbol map, which displaces the symbol's location based on the amount of overlap between neighbouring circles. At the same time, it preserves the location of non-overlapping symbols, which distinguishes it from the circular cartogram. The displacement is automated through the proximity stress model algorithm for node overlap removal. This algorithm was originally designed for graph layouts with overlapping nodes, but was modified here for circular symbols and map layout. The result is a map with improved clarity and the ability to add labelling to a cluttered proportional circle map.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".