Evaluating a Branch-and-Bound RLT-Based Algorithm for Minimum Sum-of-Squares Clustering
Bibliographic record
Abstract
Minimum sum-of-squares clustering consists in partitioning a given set of n points into c clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Sherali and Desai (JOGO, 2005) proposed a reformulation-linearization based branch-and-bound algorithm for this problem, claiming to solve instances with up to 1,000 points. In this paper, their algorithm is investigated in further detail, reproducing some of their computational experiments. However, our computational times turn out to be drastically larger. Indeed, for two data sets from the literature only instances with up to 20 points could be solved in less than 10 h of computer time. Possible reasons for this discrepancy are discussed. The effect of a symmetry breaking rule due to Plastria (EJOR, 2002) and of the introduction of valid inequalities of the convex hull of points in two dimensions which may belong to each cluster is also explored.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 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".