How the initialization affects the stability of the қ-means algorithm∗

Sébastien Bubeck; Marina Meilă; Ulrike von Luxburg

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 436-452
  • ISSN: 1292-8100

Abstract

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We investigate the role of the initialization for the stability of the қ-means clustering algorithm. As opposed to other papers, we consider the actual қ-means algorithm (also known as Lloyd algorithm). In particular we leverage on the property that this algorithm can get stuck in local optima of the қ-means objective function. We are interested in the actual clustering, not only in the costs of the solution. We analyze when different initializations lead to the same local optimum, and when they lead to different local optima. This enables us to prove that it is reasonable to select the number of clusters based on stability scores.

How to cite

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Bubeck, Sébastien, Meilă, Marina, and von Luxburg, Ulrike. "How the initialization affects the stability of the қ-means algorithm∗." ESAIM: Probability and Statistics 16 (2012): 436-452. <http://eudml.org/doc/222461>.

@article{Bubeck2012,
abstract = {We investigate the role of the initialization for the stability of the қ-means clustering algorithm. As opposed to other papers, we consider the actual қ-means algorithm (also known as Lloyd algorithm). In particular we leverage on the property that this algorithm can get stuck in local optima of the қ-means objective function. We are interested in the actual clustering, not only in the costs of the solution. We analyze when different initializations lead to the same local optimum, and when they lead to different local optima. This enables us to prove that it is reasonable to select the number of clusters based on stability scores.},
author = {Bubeck, Sébastien, Meilă, Marina, von Luxburg, Ulrike},
journal = {ESAIM: Probability and Statistics},
keywords = {Clustering; қ-means; stability; model selection; clustering; -means},
language = {eng},
month = {9},
pages = {436-452},
publisher = {EDP Sciences},
title = {How the initialization affects the stability of the қ-means algorithm∗},
url = {http://eudml.org/doc/222461},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Bubeck, Sébastien
AU - Meilă, Marina
AU - von Luxburg, Ulrike
TI - How the initialization affects the stability of the қ-means algorithm∗
JO - ESAIM: Probability and Statistics
DA - 2012/9//
PB - EDP Sciences
VL - 16
SP - 436
EP - 452
AB - We investigate the role of the initialization for the stability of the қ-means clustering algorithm. As opposed to other papers, we consider the actual қ-means algorithm (also known as Lloyd algorithm). In particular we leverage on the property that this algorithm can get stuck in local optima of the қ-means objective function. We are interested in the actual clustering, not only in the costs of the solution. We analyze when different initializations lead to the same local optimum, and when they lead to different local optima. This enables us to prove that it is reasonable to select the number of clusters based on stability scores.
LA - eng
KW - Clustering; қ-means; stability; model selection; clustering; -means
UR - http://eudml.org/doc/222461
ER -

References

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  11. O. Shamir and N. Tishby, Cluster stability for finite samples, in Proc. of NIPS (2008).  
  12. O. Shamir and N. Tishby, Model selection and stability in қ-means clustering, in Proc. of COLT (2008).  
  13. O. Shamir and N. Tishby, On the reliability of clustering stability in the large sample regime, in Proc. of NIPS (2008).  
  14. N. Srebro, G. Shakhnarovich and S. Roweis, An investigation of computational and informational limits in Gaussian mixture clustering, in Proc. of ICML (2006).  
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