Geometry/topology Seminar
Tuesday, October 27, 2009, 4:30pm, 119 Physics
Mauro Maggioni (Duke)
On estimating intrinsic dimensionality of noisy high-dimensional data sets

Abstract:

We discuss recent and ongoing work, joint with A. Little, on estimating the intrinsic dimensionality of data sets assumed to be sampled from a low-dimensional manifold in high dimensions and perturbed by high-dimensional noise. This work is motivated by several applications, including machine learning and dynamical systems, and by the limitations of existing algorithms. Our approach is based on a simple tool such as principal component analysis, used in a multiscale fashion, a strategy which has its roots in geometric measure theory. The theoretical analysis of the algorithm uses tools from random matrix theory and exploits concentration of measure phenomena in high-dimensions. The talk will have a tutorial flavour: no previous knowledge of what mentioned above will be required, and several toy examples to build intuition about some measure-geometric phenomena in high-dimensions will be presented. [video]

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