Computational and Statistical Aspects of Topological Data Analysis

Date: 23 – 24 March 2017

Time: 9:45 – 19:00 / 10:00 – 17:00

REGISTER AGENDA SUMMARIES


Topological Data Analysis (TDA) aims to describe the shape of a given dataset without making any prior assumptions or imposing a generative model. The vanguard technique in TDA is persistent homology, which collates the appearance and disappearance of intrinsic features such as components, tunnels and cavities in the data across various scales. Persistent homology has been successfully applied to real-world problems across a stunning diversity of disciplines, including graph reconstruction, signal processing, complex network analysis and disease propagation.

The goal of this two-day workshop is to explore the linear-algebraic optimizations involved in the efficient computation of persistent homology, as well as its interactions with other branches of mathematics and statistics. In particular, we hope to provide:

1. An introduction to the fundamentals of TDA and the popular software packages.
2. An overview of the matrix-based algorithms that compute persistent homology.
3. Interesting links between TDA and other data analysis methodologies.

This workshop is intended for a broad audience, with (some) knowledge of linear algebra and an open mind. We encourage PhD students, research fellows, faculty and industry partners to attend.

Schedule:

  • Recent Algorithmic Advances in TDA
    – Michael Kerber, Graz University of Technology
  • Data, Shape, Computations and Science
    – Pawel Dlotko, Swansea University
  • Ripser: Efficient Computation of Vietoris–Rips Persistence Barcodes
    – Ulrich Bauer, Technical University of Munich
  • Combinatorial Homology: A Simplified Approach to Persistence and Computation, via Matroids
    – Gregory Henselman, Princeton University
  •  Hierarchical Estimation and Learning via Topology
    – Subramanian Ramamoorthy, University of Edinburgh
  • Small versus Large Scale Features: Comparing the Appropriate Data Analysis Methods
    – Katharine Turner, École Polytechnique Fédérale de Lausanne
  • Computing Multidimensional Persistent Homology
    – Matthew Wright, St Olaf College

 

Organisers:

Heather Harrington, University of Oxford
Vidit Nanda, The Alan Turing Institute and University of Oxford
Jared Tanner, The Alan Turing Institute and University of Oxford
Ulrike Tillmann, The Alan Turing Institute and University of Oxford