Charla: “Multimodal spectral geometry of graphs and manifolds”


Compartir
Charlista: 
Michael Bronstein, Università della Svizzera Italiana
Fecha: 
22 Enero, 2014 - 12:00
Sala: 
Auditorio DCC, Piso 3
Organización: 
DCC

Abstract:

Spectral methods proved to be an important and versatile tool in a wide  range of problems in the fields of computer graphics, machine learning,  pattern recognition, and computer vision, where many important problems boil  down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions (classical examples include diffusion distances, diffusion maps, and spectral clustering). 

In this talk, I will show how to generalize spectral geometry to settings where one has multiple data spaces. Our construction of "multimodal" spectral geometry is based on the idea of simultaneous diagonalization of Laplacian operators. I will show how this problem is related to the problem of finding closest commuting operators, and discuss efficient numerical methods for its solution. As examples of applications, I will show problems from the domain of 3D shape analysis, computer vision, pattern recognition, and image processing (based on joint works with K. Glashoff, T. Loring, A. Kovnatsky, D. Eynard, R. Kimmel, A. Bronstein). 

 

---

Secretaría de Investigación