Stratification Learning: Detecting Mixed Density and Dimensionality in High Dimensional Point Clouds

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Gloria Haro, Gregory Randall, Guillermo Sapiro


The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.