TUTORIAL - Track 1

Topological Data Analysis

Yuliy Baryshnikov and Yuriy Mileyko

Sunday June 29, 2014
13:30 - 16:30
Room: 316A

Abstract:

Topological Data Analysis emerged over the past decade as a compelling alternative to the traditional tools of data science in the situations where the "big picture" is more relevant than the details, but where mere clustering is not enough. Topological Data Analysis aims at the recovery of the shape of the parameter space underlying the observed data points, be that point clouds, trajectories or fields.

In this tutorial we will survey the basic tools of TDA. We will cover classical discrete invariants of shapes (dimension, Euler characteristic, Betti numbers), explain two views on the dimensionality reduction: extrinsic (PCA, kernel methods, etc) and intrinsic (Eigenmap, Isomap, LLE), review important questions related to clustering, and introduce persistent homology.

We will illustrated the usage of the developed tools on several concrete examples. In particular, we will take a look at how to create a new toolbox for codifying the shapes, answer important questions about topology of the Internet, and detect cyclicity and transience in time-varying signals.

No knowledge of algebraic topology is assumed.

Biographies:

Yuliy Baryshnikov grew up in Moscow, then in Soviet Union, and got his PhD in applied mathematics, from Institute of Control Sciences in Moscow, in 1987. He spent his Humboldt Research Fellowship at the University of Osnabruck in Germany, then worked as a faculty member in the Netherlands, UK and France, before joining Bell Labs in Murray Hill, NJ in 2001. In 2011 he resigned from his position as a department head there and moved West, to become professor of mathematics and electrical and computer engineering at the University of Illinois at Urbana-Champaign.

His research interests include probability theory, singularities, dynamical systems, combinatorics. Among applied areas his favorites are sensor networks, nonlinear control, mathematical economics, self-assembly.

Yuriy Mileyko received his PhD in Mathematical Sciences from New Jersey Institute of Technology and Rutgers University in 2005. After that he held postdoctoral positions at Duke University, Georgia Institute of Technology and the University of Illinois at Urbana-Champaign. In Fall of 2013 he joined the Department of Mathematics at the University of Hawai'i at Manoa as an assistant professor.

His research interests include applied and computational topology, mathematical biology, and dynamical systems, with a large part of the research focused on questions related to topological data analysis, network analysis, and, more recently, multi-agent systems.