# 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/273610>.

@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; -means},

language = {eng},

pages = {436-452},

publisher = {EDP-Sciences},

title = {How the initialization affects the stability of the қ-means algorithm},

url = {http://eudml.org/doc/273610},

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

PY - 2012

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; -means

UR - http://eudml.org/doc/273610

ER -

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