A Clustering Validity Index With Multi-Granularity Fusion for Multiple Fuzzy Clustering Algorithms
Bibliographic record
Abstract
Most clustering validity indexes (CVIs) for fuzzy clustering are based upon the fuzzy c-means (FCMs) algorithm, and the effect of these CVIs is limited due to the "uniform effect" of FCM. Besides, main existing CVIs have the problems of incompleteness characterization of separateness and weak performance for noisy datasets. To address these challenges, the multi-granularity fusion (MGF) index is proposed. First, MGF synthetically considers the FCM, possibilistic fuzzy c-means and kernel-based FCM algorithms, which is more comprehensive than just considering FCM. Second, we add a perturbation to the sum of the partition matrix as the fuzzy cardinality and combine it with the fuzzy weighted distance, which are helpful to grasp the compactness. Third, four elements are considered together to characterize the separateness, incorporating the minimum distance, the maximum distance, the mean distance, and the sample variance of cluster center, where the last one can make the separateness unbiased from the macroscopic perspective. Besides, the convergence of MGF is proved. Finally, we test MGF for five algorithms on 36 datasets comparing with 14 CVIs, validating the accuracy and stability of MGF. It is observed that MGF can get superior results than other CVIs, especially for high-dimensional datasets and noisy datasets.
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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 | 0.010 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.011 | 0.009 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".