How the initialization affects the stability of the k-means algorithm
ESAIM: Probability and Statistics, Volume 16 (2012), pp. 436-452.

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.

DOI: 10.1051/ps/2012013
Classification: 62F12
Keywords: clustering, қ-means, stability, model selection
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     title = {How the initialization affects the stability of the $k$-means algorithm},
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Bubeck, Sébastien; Meilă, Marina; von Luxburg, Ulrike. How the initialization affects the stability of the $k$-means algorithm. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 436-452. doi : 10.1051/ps/2012013. http://archive.numdam.org/articles/10.1051/ps/2012013/

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