Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given independent observations drawn from an unknown multivariate probability density , we propose a new approach to estimate the number of connected components, or clusters, of the -level set . The basic idea is to form a rough skeleton of the set using any preliminary estimator of , and to count the number of connected components of the resulting graph. Under mild analytic conditions on , and using tools from differential geometry, we establish the consistency of our method.
Mots-clés : cluster analysis, connected component, level set, graph, tubular neighborhood
@article{PS_2007__11__272_0,
author = {Biau, G\'erard and Cadre, Beno{\^\i}t and Pelletier, Bruno},
title = {A graph-based estimator of the number of clusters},
journal = {ESAIM: Probability and Statistics},
pages = {272--280},
publisher = {EDP-Sciences},
volume = {11},
year = {2007},
doi = {10.1051/ps:2007019},
mrnumber = {2320821},
zbl = {1187.62114},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2007019/}
}
TY - JOUR AU - Biau, Gérard AU - Cadre, Benoît AU - Pelletier, Bruno TI - A graph-based estimator of the number of clusters JO - ESAIM: Probability and Statistics PY - 2007 SP - 272 EP - 280 VL - 11 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007019/ DO - 10.1051/ps:2007019 LA - en ID - PS_2007__11__272_0 ER -
%0 Journal Article %A Biau, Gérard %A Cadre, Benoît %A Pelletier, Bruno %T A graph-based estimator of the number of clusters %J ESAIM: Probability and Statistics %D 2007 %P 272-280 %V 11 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2007019/ %R 10.1051/ps:2007019 %G en %F PS_2007__11__272_0
Biau, Gérard; Cadre, Benoît; Pelletier, Bruno. A graph-based estimator of the number of clusters. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 272-280. doi : 10.1051/ps:2007019. http://www.numdam.org/articles/10.1051/ps:2007019/
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