Topic

There is a growing interest in Machine Learning, in applying geometrical and topological tools to high-dimensional data analysis and processing. 
Considering a finite set of points in a high-dimensional space, the approaches developed in the field of Topology Learning intend to learn, explore and exploit the topology of the shapes (topological invariants such as the connectedness, the intrinsic dimension or the Betti numbers), manifolds or not, from which these points are supposed to be drawn.

Applications likely to benefit from these topological characteristics have been identified in the field of Exploratory Data Analysis, Pattern Recognition, Process Control, Semi-Supervised Learning, Manifold Learning and Clustering. 

However it appears that the integration in the Machine Learning and Statistics frameworks of the problems we are faced with in Topology Learning, is still in its infancy. So we wish this workshop to ignite cross-fertilization between Machine Learning, Computational Geometry and Topology, likely to benefit to all of them by leading to new approaches, deeper understanding, and stronger theoretical results about the problems carried by Topology Learning.

Trends

We wish this workshop to do the spadework on the following open problems and discuss the proposed solutions:

• Theory: How and under which conditions to ensure provably correct topology with respect to the data? Especially facing noisy, multi-scale, multidimensional or incomplete datasets?

• Algorithms: How to cope with multidimensional or massive datasets in reasonable memory and time? Can we provide objective criteria to tune the hyper-parameters?

• Applications: How can we insert the topological knowledge into Machine Learning algorithms? When is it beneficial to do so? How to visually represent the resulting topology to the analyst in case of exploratory data analysis? Can we define some benchmark of real and artificial data specific to this field?

 

Submission

Authors are invited to submit an abstract based on original research or already published results, describing new methods they developed, open problems they are faced with or applications they tackle, fitting the topic and trends given above. Abstracts should not exceed 2 single-spaced pages with figures and references. If the authors believe that more details are essential to substantiate the main claims of their abstract, they may include a clearly marked appendix that will be read at the discretion of the scientific committee.

Abstracts shall be sent by e-mail to: topolearn2007@gmail.com with subject "SUBMIT".

 

Important dates

• Submission of abstracts: before October 12, 2007

• Notification of acceptance: October 19, 2007

• Workshop on Topology Learning: December 7-8, 2007

Invited speakers

Pr. Herbert Edelsbrunner (Duke Univ., NC, USA, http://www.cs.duke.edu/~edels/) Research on algebraic topological tools for high dimensional data analysis and the study of families of shapes.

Pr. Mathias Hein (Saarland Univ., Saarbrücken, Germany, http://www.kyb.mpg.de/~mh)  - Pascal Network Member            Research on semi-supervised learning and kernel-based algorithms.

Pr. Partha Niyogi (Univ. of Chicago, IL, USA, http://people.cs.uchicago.edu/~niyogi/)              Research on Machine Learning and Information Extraction.

Pr. Jean-Daniel Boissonnat (INRIA Sophia Antipolis, France, http://www.inria.fr/personnel/Jean-Daniel.Boissonnat.en.html )          Research on Geometric Computing.

Dr. Vin de Silva (Pomona College, CA, USA, http://pages.pomona.edu/~vds04747/public/index.html)           Research on Computational and Statistical Topology.