Topology and Big Data

DMV-Studierendenkolleg

There will be introductory lectures on persistent homology, aimed at students at all levels (bachelor, master and PhD) who are interested in applications of algebraic topology, assuming only knowledge of point-set topology and the concept of homology.

Date and venue: 23.2.2015, Freiburg im Breisgau (H├Ârsaal II, Albertstr. 23b)

Topic: Topological Data Analysis and Persistent Homology
Recently science and industry deals with growing amount of data, often of high dimensionality, termed "big data", coming for example from experiments in biology or computer vision.

These huge amounts of data are usually modelled as point clouds in a high-dimensional vector space. One way to understand something about the data is to find a geometric object for which the data looks like a sampling of points. Then the geometric object is seen as an interpolation of the data.

Topology is the study of qualitative features of geometric objects, and algebraic topology is the art of presenting such qualities as algebraic information which one may try to compute, with homology theories being among the most important examples. One should expect that algebraic topology is also useful in studying the qualitative features of big data.

The easiest example of a topological approach to data is clustering, where one groups together data points according to a loose notion of proximity. This corresponds to computing the zeroth homology of a geometric object interpolating the data points.

Persistence is the philosophy of not choosing just one geometric object to model the data, but a whole family, parameterized by how close two data points have to be, to be considered topologically close in the geometric model. Technically, one defines a simplicial complex by connecting points which are close enough.

There's also a poster to print out available.

Schedule:

  • 9:00 - 10:00 -- Wolfgang Soergel (Freiburg) Recollection on homology of simplicial complexes
  • 10:00 - 10:30 -- Coffee break
  • 10:30 - 12:00 -- Jan Senge (CALTOP Bremen): Introduction to
       Topological Data Analysis and Persistent Homology
  • 12:00 - 13:30 -- Lunch break
  • 13:30 - 15:00 -- Michael Kerber (MPI Saarbr├╝cken): Introduction to
       Topological Data Analysis and Persistent Homology
  • 15:00 - 16:00 -- Coffee and discussion

Registration: We would very much welcome an e-mail to one of the organizers, but you may as well just show up. As a rule, you arrive with your own funding. The speakers are funded by the Graduiertenkolleg GK1821 of the DFG. There is funding from the DMV, to support travelling students, i.e. you can get your train/bus ticket refunded.

Organizers: Anja Wittmann, Konrad Voelkel

Funding is generously provided by the
DMV
(Deutsche Mathematiker-Vereinigung)

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