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# Adaptive Density Level Set Clustering

*Proceedings of the 24th Annual Conference on Learning Theory*, PMLR 19:703-738, 2011.

#### Abstract

Clusters are often defined to be the connected components of a density level set.Unfortunately, this definition depends on a level that needs to be user specifiedby some means. In this paper we present a simple algorithm that is able to asymptotically determinethe optimal level, that is, the level at which there is the first split in the cluster treeof the data generating distribution. We further show that this algorithm asymptotically recoversthe corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness.