Optimal and Greedy Algorithms for Clustering with Applications to Data Science
Bibliographic record
Abstract
Clustering is a fundamental task in unsupervised learning and is popularly used in numerous scientific fields for exploratory data analysis and data science to discover latent discrete class structures. However, despite its maturity as a field, there remain several unanswered research questions and avenues for exploration such as (1) the absence of scalable and optimal algorithms for widely used methods like k-center clustering, and (2) the relatively unexplored space of models for clustering w.r.t. supervised learning objectives. To this end, this thesis addresses some of these open questions by (1) presenting a novel highly scalable algorithm that leverages constraint generation and mixed integer linear programming to efficiently and provably converge to global optimum for the generalized k-center objective, and (2) proposing a generalized optimization framework for predictive (supervised) clustering that admits different cluster definitions (arbitrary point assignment, closest center, bounding box) for both regression and classification objectives. These models help uncover different interpretable discrete cluster structures in data. Overall, this thesis makes advances in two critical areas of clustering that have the potential to provide strong guarantees for optimal clustering and provide a design space and toolkit of supervised clustering models for data science practitioners.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| 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".