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Topological data analysis is a new area which seeks to apply methods from topology to study the "shape" of data sets. It is particularly suited to noisy data sets sitting in potentially high (e.g., 10,000) dimensional spaces, which are none-the-less concentrated around low-dimensional geometric structures that need to be uncovered. Despite being a new area, topological data analysis has already seen applications in several areas of science and engineering, including oncology, astronomy, neuroscience, image processing, and biophysics. For more information see:http://www.mi.fu-berlin.de/users/shanekelly/TopologicalDataAnalysis2017SS.html
Aimed at: Bachelor and masters students (of mathematics, computer science, physics, etc) Background: A knowledge of linear algebra is sufficient. The course does not require any previous knowledge of topology or statistics.
Topological data analysis is a new area which seeks to apply methods from topology to study the "shape" of data sets. It is particularly suited to noisy data sets sitting in potentially high (e.g., 10,000) dimensional spaces, which are none-the-less concentrated around low-dimensional geometric structures that need to be uncovered.
Despite being a new area, topological data analysis has already seen applications in several areas of science and engineering, including oncology, astronomy, neuroscience, image processing, and biophysics.
For more information see: http://www.mi.fu-berlin.de/users/shanekelly/TopologicalDataAnalysis2017SS.html
Additional info and prerequisites:
Literature:
Geometric and Topological Inference by Boissonnat and Chazal and Yvinec,
Topology and data by Gunnar Carlsson,
Principal Component Analysis of Persistent Homology Rank Functions by Robins and Turner
Course texts: 1. Geometric and Topological Inference by Boissonnat and Chazal and Yvinec 2. Topology and data by Gunnar Carlsson 3. Principal Component Analysis of Persistent Homology Rank Functions by Robins and Turner