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In the context of clustering, we consider a generative model in a Euclideanambient space with clusters of different shapes, dimensions, sizes anddensities. In an asymptotic setting where the number of points becomes large,we obtain theoretical guaranties for a few emblematic methods based on pairwisedistances: a simple algorithm based on the extraction of connected componentsin a neighborhood graph; the spectral clustering method of Ng, Jordan andWeiss; and hierarchical clustering with single linkage. The methods are shownto enjoy some near-optimal properties in terms of separation between clustersand robustness to outliers. The local scaling method of Zelnik-Manor and Peronais shown to lead to a near-optimal choice for the scale in the first twomethods. We also provide a lower bound on the spectral gap to consistentlychoose the correct number of clusters in the spectral method.

Clustering Based on Pairwise Distances When the Data is of Mixed Dimensions