On k-means iterations and Gaussian clusters
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Bibliographic record
Abstract
Nowadays, k-means remains arguably the most popular clustering algorithm [1], [2]. Two of its main properties are simplicity and speed in practice. Here, our main claim is that the average number of iterations k-means takes to converge (τ¯) is in fact very informative. We find this to be particularly interesting because τ¯ is always known when applying k-means but has never been, to our knowledge, used in the data analysis process. By experimenting with Gaussian clusters, we show that τ¯ is related to the structure of a data set under study. Data sets containing Gaussian clusters have a much lower τ¯ than those containing uniformly random data. In fact, we go considerably further and demonstrate a pattern of inverse correlation between τ¯ and the clustering quality. We illustrate the importance of our findings through two practical applications. First, we describe the cases in which τ¯ can be effectively used to identify irrelevant features present in a given data set or be used to improve the results of existing feature selection algorithms. Second, we show that there is a strong relationship between τ¯ and the number of clusters in a data set, and that this relationship can be used to find the true number of clusters it contains.
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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 | 0.000 | 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 | 0.000 | 0.001 |
| 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