Cumulative Voting Consensus Method for Partitions with Variable Number of Clusters
Bibliographic record
Abstract
Over the past few years, there has been a renewed interest in the consensus clustering problem. Several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble. In this paper, we propose new consensus clustering algorithms with linear computational complexity in n. We consider clusterings generated with random number of clusters, which we describe by categorical random variables. We introduce the idea of cumulative voting as a solution for the problem of cluster label alignment, where, unlike the common one-to-one voting scheme, a probabilistic mapping is computed. We seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble, where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy. We describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble. Given the arbitrary number of clusters of the input partitions, we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves maximum relevant information. An efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized Jensen-Shannon divergence within the cluster. The empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".