The X-Alter algorithm : a parameter-free method to perform clustering
Résumé
Using quantization techniques, Laloë (2009) defined a new algorithm called Alter. This $L^1$-based algorithm is proved to be convergent, but suffers two shortcomings. Firstly the number of clusters $K$ has to be supplied by the user. Secondly it has an high complexity. In this article, we adapt the idea of $X$-means algorithm (Pelleg and Moore; 2000) to offer solutions for these problems. This fast algorithm is used as a building-block which quickly estimates $K$ by optimizing locally the Bayesian Information Criterion (BIC). Our algorithm combines advantages of $X$-means (calculation of $K$ and speed) and Alter (convergence and parameter-free). Finally, an aggregative step is performed to adjust the relevance of the final clustering according to BIC criterion. We confront here our algorithm to different simulated data sets, which show its relevance.
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