An introduction to Topological Data Analysis

An introduction to Topological Data Analysis

An introduction to Topological Data Analysis


Big Data analysis is becoming one of the hottest topics in current research in applicable mathematics. Information extracted from Big datasets plays a key role in the understanding of complex processes in a wide range of fields such as biomedicine, e-commerce, and industry.
The need of methods that can handle with big data sets more efficiently and exploit the extra information that high dimensional data offer has lead to a revolution in analytical data sciences. Besides machine and statistical learning, geometry and topology are very natural tools to apply in this direction, since geometry can be regarded as the study of distance functions, and what one often works with are distance functions on large finite sets of data.
Topological Data Analysis (TDA) is a recent field whose aim is to uncover, understand and exploit the topological and geometric structure underlying complex and possibly high dimensional data. It proposes new well-founded mathematical theories and computational tools that can be used independently or in combination with other data analysis and statistical learning techniques. Interestingly, TDA set of tools for dimensional reduction and visualisation of high dimensional data have shown a big potential to unlock relationships that would be considered as noise by traditional statistical approaches as traditional clustering.
TDA has been attracting a lot of interest during the recent years but it still appears difficult to access for data scientists with low expertise in topology or geometry. The goal of this course is to make the fundamentals of TDA accessible to a large audience (with a minimal mathematical background). For that purpose, the focus will be put on the practical aspects of the field rather than very theoretical considerations. The course will be organized around the following topics that play a central role in TDA.
     1. Mapper as a topological tool for data exploration and visualization.
     2. Persistent homology: an introduction (simplicial complexes, filtrations, homology,…).
     3. Applications of persistent homology in TDA: clustering, topological signatures, statistical aspects,…
     4. Distance-to-Measure and geometric inference.

Frédéric Chazal – INRIA – DataShape team

Bertrand Michel – Université Pierre et Marie Curie – DataShape team

Albert Ruiz – UAB – Mathematics Department, Algebraic Topology group

Raquel Iniesta – King’s College London – Department of Medical and Molecular genetics – Statistical Genetics Unit


Detalles de organización:

El Curso de An introduction to Topological Data Analysis se impartirá los días 6, 7 y 8 de junio de 2016 de 9:30 a 13:30.


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