Focus on a joint research project: COMET

COMET (2011-2013)

Computational methods for the analysis of high-dimensional data

Principal Investigators :

  • Dr. Steve Y. Oudot, GEOMETRICA project-team, Inria Saclay Ile de France
  • Prof. Leonidas Guibas, Stanford University
  • Prof. Yusu Wang, Ohio-State University

Research objectives:

COMET is an Associate Team between the GEOMETRICA group at Inria, the Geometric Computing group at Stanford University, and the Computational Geometry group at the Ohio State University. Its focus is on the design of computational methods for the analysis of high dimensional data, using tools from metric geometry and algebraic topology. The goal of the team is to extract enough structure from the data, so as to get a higher level informative understanding of these data and of the spaces they originate from. The main challenge is to be able to go beyond mere dimensionality reduction and topology inference, without the need for a costly explicit reconstruction.

Scientific achievements:

COMET focused on the following topics:
  • Analysis of shapes via signatures: Analysis and visualization of maps between shapes, and Map-based exploration of intrinsic shape differences and variability.
  • Geometric and topological inference in the presence of noise and outliers: Smoothing GPS trajectories using distances to measures, Reconstructing metric graphs from point cloud data, Clustering point cloud data using topological persistence, Homology inference in the presence of unbounded noise and outliers, and Scalar fields analysis in the presence of unbounded noise and outliers.

Publications and Awards:

Selected publication:

F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba. Persistence-Based Clustering in Riemannian Manifolds. Journal of the ACM, volume 60, issue 6, article 41, 2013.

Follow up:

The work done between Inria and Stanford within COMET has given promising results, while the 2 topics addressed would benefit greatly from being considered jointly instead of separately.

More about COMET: