B0819
Title: Statistical learning for shape analysis via persistence diagrams
Authors: Steve Oudot - INRIA Saclay (France)
Maks Ovsjanikov - LIX Ecole Polytechnique (France)
Mathieu Carriere - INRIA Saclay (France) [presenting]
Abstract: A novel way is presented to use topological tools, the so-called persistence diagrams, in machine learning. More precisely, a construction is introduced that maps these objects to finite dimensional normed vector spaces while preserving the stability properties they enjoy. The construction is flexible in the sense that the dimension of the target space can be reduced at will while preserving the stability guarantees. Furthermore, it allows to use all classical kernel methods on the persistence diagrams directly. Then, results in two applications coming from shape analysis are shown: 3d shape matching and shape segmentation, via the use of kernel Support Vector Machines.
