Ellipsoidal K-Means: An Automatic Clustering Approach for Non-Uniform Data Distributions
Bibliographic record
Abstract
Traditional K-means clustering assumes, to some extent, a uniform distribution of data around predefined centroids, which limits its effectiveness for many realistic datasets. In this paper, a new clustering technique, simulated-annealing-based ellipsoidal clustering (SAELLC), is proposed to automatically partition data into an optimal number of ellipsoidal clusters, a capability absent in traditional methods. SAELLC transforms each identified cluster into a hyperspherical cluster, where the diameter of the hypersphere equals the minor axis of the original ellipsoid, and the center is encoded to represent the entire cluster. During the assignment of points to clusters, local ellipsoidal properties are independently considered. For objective function evaluation, the method adaptively transforms these ellipsoidal clusters into a variable number of global clusters. Two objective functions are simultaneously optimized: one reflecting partition compactness using the silhouette function (SF) and Euclidean distance, and another addressing cluster connectedness through a nearest-neighbor algorithm. This optimization is achieved using a newly-developed multiobjective simulated annealing approach. SAELLC is designed to automatically determine the optimal number of clusters, achieve precise partitioning, and accommodate a wide range of cluster shapes, including spherical, ellipsoidal, and non-symmetric forms. Extensive experiments conducted on UCI datasets demonstrated SAELLC’s superior performance compared to six well-known clustering algorithms. The results highlight its remarkable ability to handle diverse data distributions and automatically identify the optimal number of clusters, making it a robust choice for advanced clustering analysis.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".