Topological Data Analysis - applying homology in medicine, robotics, sensor networks, and graphics

Dr Mikael Vejdemo Johansson (KTH, Stockholm)

Friday 22nd February, 2013 16:00-17:00 Mathematics 516


In recent decades, computation and data analysis techniques have matured to the point where our entire society runs on machine learning and data analysis — the commercials you see are generated from analyses of your shopping behavior, your travel is optimized with data collected from past travel intensities, the medical care you receive is optimized by data-intensive studies of various kinds. Data becomes available at high volume and high speed, and techniques to deal with data grow by leaps and bounds. In the past decade, various approaches to data analysis rooted in algebraic topology have gained traction as a vital research field. Already clustering — a powerful family of methods with ubiquitous application — is an essentially topological technique, and generalizations are increasingly useful. We shall look at the foundations of these generalized applied topology methods in some detail, and see how they have been applied in the past. Along the journey, we shall meet classifications of breast cancer types, statistics of naturally occurring images, approaches to understanding how languages encode color, and methods for understanding periodicity in complex systems.

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