Workshop 2: Manifold Learning

Date: May 30 - June 3, 2011
Venue: HIM lecture hall, Poppelsdorfer Allee 45
Organizers: Jochen Garcke, Michael Griebel

In the field of manifold learning, non-linear methodologies are investigated to efficiently describe high-dimensional data by lower dimensional structures. The research is motivated by the observation made in many data driven research fields that a rich structure is present in the application data which can and needs to be exploited for an efficient representation.

In recent years several new machine learning algorithms were introduced which allow such a nonlinear dimension reduction. They aim to exploit local structure and estimations of the intrinsic geometry, dimension, or topology. Theoretical insights from topology allowed new methods for dimensionality estimation. New regularization approaches for classification and regression which take the geometry into account are also closely related to manifold learning.

The workshop brought together researchers interested in manifold learning and dimension reduction. Due to the diverse nature of the field this includes, but is not limited to, people from machine learning, numerical mathematics, linear algebra, topology, geometry, or statistics.

Some of the key topics to be featured were

  • applications of manifold learning to real world problems
  • theoretical limitations of current algorithms
  • connections between the different algorithms
  • dimensionality estimation
  • efficient realization of manifold learning algorithms