Modeling Noisy Data : Towards a Generic Framework Coupling Morse Theory and Persistence Theory

Google Tech Talk March 23, 2012 Presented by Frédéric Cazals. ABSTRACT Noisy data are commonplace in science and engineering, and the importance of developing robust non-parametric models for such data cannot be overstated. In this talk, we shall review recent concepts and algorithms developed in computational geometry and computational topology for three seemingly unrelated problems in the realm of noisy data modeling, namely reconstructing sampled compact sets from R^3, modeling fuzzy (molecular) objects in R^3 and, and investigating high dimensional terrains with applications in biophysics and non convex optimization. Remarkably, we shall see that all solutions follow the same pattern, which consists of three steps, namely (i) defining a generalized distance function, (ii) constructing (a subset of) the Morse-Smale diagram of this function, and (iii) extracting stable features applying topological persistence on the Morse-Smale complex. Speaker Info: Frédéric Cazals is research director at INRIA Sophia Antipolis - Méditerranée, France, where he leads the Algorithms-Biology-Structure group (ABS). He holds an engineering degree in Biological Sciences from the Institut National Agronomique Paris-Grignon (Paris, France), a master degree in theoretical computer science from Ecole Normale Supérieure and Ecole Polytechnique (Paris, France), and a PhD in theoretical computer science from the University of Paris VII (Paris, France). His research interests encompass computational structural biology (modeling protein complexes and assemblies, modeling the flexibility of proteins), as well as geometric and topological modeling (applied differential geometry, computational geometry, computational topology, shape learning).