Optimized Centroid-Based Clustering of Dense Nearly-square Point Clouds by the Hexagonal Pattern
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Bibliographic record
Abstract
Abstract An approach to optimize centroid-based clustering of flat objects is suggested, which is practically important for efficiently solving metric facility location problems. In such problems, the task is to find the best warehouse locations to optimally service a given set of consumers. An example is assigning mobiles to base stations of a wireless communication network. We suggest a hexagonal-pattern-based approach to partition flat nodes into clusters quicker than the k -means algorithm and its modifications do. First, a hexagonal cell lattice is applied to nodes to approximately determine centroids of the clusters. Then the centroids are used as initial centroids to start the k -means algorithm. The suggested method is efficient for centroid-based clustering of dense nearly-square point clouds of 0.1 million points and greater by using no fewer than 6 lattice cells along an axis. Compared to k -means, our method is at least 10 % faster and it is about 0.01 to 0.07 % more accurate in regular Euclidean distances. In squared Euclidean distances, the accuracy gain is 0.14 to 0.21 %. Applying a hexagonal cell lattice determines an upper bound of the clustering quality gap.
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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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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