On September 3, 2009 Mauro Maggioni will be leading a discussion on Some questions about the geometry of noisy high-dimensional data sets.

Location: 4219 French Family Science Center

Time: 1:00 – 2:00 pm

Abstract: We discuss recent and ongoing work aimed at studying the geometry of high-dimensional data sets corrupted by noise. These data sets may arise in different settings (images, sounds, text documents, molecular configurations) but a common feature we are interested in is that they are embedded in very high-dimensional spaces, are corrupted by noise, and nevertheless they have a low intrinsic dimensionality. We will discuss several questions, among which how to try to estimate the intrinsic dimensionality of such data, how to parametrize such low-dimensional sets in a robust fashion, and how this has been benefitting algorithms in machine learning. The talk will have a tutorial-ish flavour: no previous knowledge of what is mentioned above will be required, and several toy examples to build intuition about some measure-geometric phenomena in high-dimensions will be discussed.