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Frédéric CHAZAL (INRIA) – “An introduction to persistent homology in Topological Data Analysis and the density of expected persistence diagrams “
February 5, 2018, 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 5th of February 2018
Place: Room 3001.
Frédéric CHAZAL (INRIA) “An introduction to persistent homology in Topological Data Analysis and the density of expected persistence diagrams “
Abstract:Persistence diagrams play a fundamental role in Topological Data Analysis (TDA) where they are used as topological descriptors of data represented as point cloud. They consist in discrete multisets of points in the plane $\R^2$ that can equivalently be seen as discrete measures in $\R^2$. In a first part of the talk, we will introduce the notions of persistent homology and persistence diagrams and show how they are built from point cloud data (so no knowledge in TDA is required to follow the talk). In the second part of the talk we will show a few properties of persistence diagrams when the data come as a random point cloud. In this case, persistence diagrams become random discrete measures and we will show that, in many cases, their expectation has a density with respect to Lebesgue measure in the plane and we will discuss its estimation.
This is a joint work with Vincent Divol (ENS Paris / Inria DataShape team)
Cristina BUTUCEA, Alexandre TSYBAKOV, Eric MOULINES, Mathieu ROSENBAUM