Topological Data Analysis for Curve Classification (In progress)

12 Mai 2022 - 00:00:00
17:00
Salón de Graos, Facultade de Matemáticas USC

Topological Data Analysis for Curve Classification (In progress)

Topological Data Analysis for Curve Classification (In progress), given by Fatemeh Razeghi, Universidade de Santiago de Compostela (USC).

Fecha: 12 de mayo

Hora: 17:00 h.

Lugar: Salón de Grados, Facultad de Matemáticas USC

Duración: 1 hora

Abstract: In this presentation I will show how it is possible to extract topological information from a cloud of points of a metric space by using algebraic topology techniques. In particular, I will introduce you to what simplicial complexes are and how to encode a topological space using them. Afterwards, I will explain how to calculate the persistent homology of a filtered simplicial complex and how this technique allows us to convert topological information encoded in a cloud of points into a diagram called persistent diagram and how to do this. All of this is included in what is called Topological Data Analysis (TDA).

Finally, I will present how I am using TDA to achieve first goal in my research: to find out if it is possible to distinguish closed curves in R^3 by applying Topological Data Analysis techniques on a set of random points (plus noise) taken from them. Also I am interested in testing the “limits” of the method.

 

Actividade co-financiada coa colaboración da Consellería de Cultura, Educación, Formación Profesional e Universidades