Blind method for discovering number of clusters in multidimensional datasets by regression on linkage hierarchies generated from random data
Bibliographic record
Abstract
Determining intrinsic number of clusters in a multidimensional dataset is a commonly encountered problem in exploratory data analysis. Unsupervised clustering algorithms often rely on specification of cluster number as an input parameter. However, this is typically not known a priori. Many methods have been proposed to estimate cluster number, including statistical and information-theoretic approaches such as the gap statistic, but these methods are not always reliable when applied to non-normally distributed datasets containing outliers or noise. In this study, I propose a novel method called hierarchical linkage regression, which uses regression to estimate the intrinsic number of clusters in a multidimensional dataset. The method operates on the hypothesis that the organization of data into clusters can be inferred from the hierarchy generated by partitioning the dataset, and therefore does not directly depend on the specific values of the data or their distribution, but on their relative ranking within the partitioned set. Moreover, the technique does not require empirical data to train on, but can use synthetic data generated from random distributions to fit regression coefficients. The trained hierarchical linkage regression model is able to infer cluster number in test datasets of varying complexity and differing distributions, for image, text and numeric data, using the same regression model without retraining. The method performs favourably against other cluster number estimation techniques, and is also robust to parameter changes, as demonstrated by sensitivity analysis. The apparent robustness and generalizability of hierarchical linkage regression make it a promising tool for unsupervised exploratory data analysis and discovery.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".