Workshop on Topological Data Analysis

Date and time: 
Mon, 2018-11-12 12:14
Location / Venue: 

School of Mathematics, Chiromo Campus, University of Nairobi

Prof. Wojciech Chachólski Department of Mathematics, KTH, Sweden, an algebraic topologist, but recently interested in mathematical aspects of Topological Data Analysis will give a course on TDA. The lectures will be entertaining for both pure and applied mathematicians and very accessible to our math graduate 
 
Detailed Course Description.
Homology, the central theme of the 20th century  geometry, has been particularly useful   for  studying  spaces with controllable  cell  decompositions such as Grassmann varieties, manifolds, Lie groups and classifying spaces of groups.  During the last decade there has been an  explosion of applications ranging from  road network reconstructions to neuroscience, vehicle tracking, object recognition, protein structure analysis and  the nano characterization of materials, testifying to usefulness of homology to understand spaces described also by measurements and samplings. One might ask: why does homology have such a central role in so many applications?
 
We commonly describe objects in our environment by quantifying some of their properties, as for example: weight, height, length. These measurements are then collected to form a dataset. Often due to heterogeneity, the presence of  noise, inconsistent data acquisition protocols and/or pre-processing steps,  it is very hard to understand our data. In this cases rather than trying to fit the data with complicated models a good strategy is to first investigate shape properties of such data. Here homology and Topological Data Analysis come into play, with a toolkit of algorithms that detect robust shape characteristics.
 
The   fundamental challenge  of using homology in data analysis is however that its outcomes are not readily suitable for statistical analysis. The objective of this course is   to explain how  homology can also be used  in supervised learning. To this purpose new continuous  homology based invariants suitable for statistical analysis  will be defined, studied and  illustrated
Expiry Date: 
Sat, 2050-11-12 12:14

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