A Distance Metric for Uneven Clusters of Unsupervised K-Means Clustering Algorithm
Bibliographic record
Abstract
In this paper, we propose a new distance metric for the K-means clustering algorithm. Applying this metric in clustering a dataset, forms unequal clusters. This metric leads to a larger size for a cluster with a centroid away from the origin, rather than a cluster closer to the origin. The proposed metric is based on the Canberra distances and it is useful for cases that require unequal size clusters. This metric can be used in connected autonomous vehicle wireless networks to classify mobile users such as pedestrians, cyclists, and vehicles. We use a combination of mathematical and exhaustive search to establish its validity as a true distance metric. We compare the K-Means algorithm using the proposed distance metric with five other distance metrics for comparison. These metrics include the Euclidean, Manhattan, Canberra, Chi-squared, and Clark distances. Simulation results depict the effectiveness of our proposed metric compared with the other distance metrics in both one-dimensional and two-dimensional randomly generated datasets. In this paper, we use three internal evaluation measures namely the Compactness, Sum of Squared Errors (SSE), and Silhouette measures. These measures are used to study the proper number of clusters for each of the K-Means algorithms and also select the best run among multiple centroid initializations. The elbow method and the local maximum approach are used alongside the evaluation measures to select the optimal number of clusters.
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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".