Descriptive Measures of Point Distributions Summarized with Respect to Spatial Scale in Visualization
Bibliographic record
Abstract
Visual exploration plays a critical role in point pattern analysis. It permits analysts to grasp a wide variety of spatial patterns in point distributions that are not necessarily detectable by mathematical and statistical methods. Since spatial patterns are scale-dependent, grid and kernel density maps are effective in analysis that can visualize point distributions at various scales from small to large. Visual exploration of these maps, however, takes a considerable amount of time even if the maps are generated automatically in GIS software. In addition, visual exploration inevitably becomes subjective and unstable when treating numerous maps simultaneously. It is not easy to evaluate and memorize spatial patterns in maps in a consistent and objective way. To resolve the problem, this article proposes new quantitative measures summarizing the characteristics of point distributions. The measures can be visualized as maps that help analysts to capture the overall spatial pattern of point distributions efficiently. Numerical experiments and applications to real data analysis are performed to test the validity of the proposed measures. The results reveal the effectiveness of the measures, as well as their shortcomings, to be resolved in future research.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".