# 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

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topBubeck, 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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