Given i.i.d. random variables X1,…,Xn ∈ ℝ^D drawn from a stratified mixture ⋃ k=1^KMk of immersed C²-manifolds of different dimensions (dk)k≤K, we study the minimax estimation of the family (Mk)k≤K and the associated unsupervised clustering problem. We provide a constructive algorithm allowing to estimate each mixture component Mk at its optimal dimension-specific rate (log(n)∕n)^2∕dk adaptively. The method is based on an ascending hierarchical co-detection of points belonging to different layers which also identifies the number of layers K, the dimensions (dk)k≤K, assign each point Xi to a layer accurately, and estimate tangent spaces optimally. The results hold regardless of any reach assumption on the Mk’s nor on intersection configurations Mk ∩ Mk^′ . They open the way to a broad clustering framework, where each mixture component (or stratum) Mk models a cluster, emanating from a specific nonlinear correlation phenomenon leaving only dk local degrees of freedom.

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