@article{2006-WeightingClustering-PAMI
, author={Richard Nock and Frank Nielsen}
, title={On weighting clustering}
, journal={IEEE Transactions on Pattern Analysis and  Machine Intelligence}
, month={August}
, year={2006}
, volume={28}
, number={8}
, pages={1223-1235}
, doi={10.1109/TPAMI.2006.168}
, abstract={
  Recent papers and patents in iterative unsupervised learning have emphasized a
 new trend in clustering. It basically consists of penalizing solutions via weights
 on the instance points, somehow making clustering move toward the hardest points
 to cluster. The motivations come principally from an analogy with powerful supervised
 classification methods known as boosting algorithms. However, interest in this analogy
 has so far been mainly borne out from experimental studies only. This paper is,
 to the best of our knowledge, the first attempt at its formalization. More precisely,
 we handle clustering as a constrained minimization of a Bregman divergence. Weight
 modifications rely on the local variations of the expected complete log-likelihoods.
 Theoretical results show benefits resembling those of boosting algorithms and bring
 modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means,
 Expectation Maximization (EM), and k-harmonic means. Experiments are provided for
 all these algorithms, with a readily available code. They display the advantages
 that subtle data reweighting may bring to clustering.
}
}