On k-means iterations and Gaussian clusters
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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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 | 0.015 | 0.064 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.004 | 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".