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The objective of this paper is to show that point cloud data can under certain circumstances be clustered by strata in a plausible way. For our purposes, we consider a stratified space to be a collection of manifolds of different dimensions which are glued together in a locally trivial manner inside some Euclidean space. To adapt this abstract definition to the world of noise, we first define a multi-scale notion of stratified spaces, providing a stratification at different scales which aredoi:10.1137/1.9781611973099.107 dblp:conf/soda/BendichWM12 fatcat:tftjltqrrrdhvimbqxmeyk3qa4