Persistent homology plays a central role in TDA by providing a powerful framework to infer relevant topological features from complex data. However, these features usually come as multisets of points in the plane, the so-called persistence diagrams, and cannot be directly processed as standard features in classical Machine Learning pipelines. Various methods have been proposed among the literature to “vectorize” persistence diagrams, but they mostly appear as ad-hoc heuristics and remain difficult to use for non-expert. In this talk, after a brief general introduction to persistent homology, we will present a few mathematical properties of the commonly used representations of persistence diagrams and show how they can be learnt from data. As an illustration, we will focus on a specific graph classification problem and show how persistence can easily lead to state-of-the-art results.
This is a joint work with Mathieu Carrière (Columbia University), Théo Lacombe and Martin Royer (Inria) and, Yiuchi Ike and Yuhei Umeda (Fujitsu Labs) [AISTATS 2020]
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*Texto informado pelo autor.
Frédéric Chazal is a Directeur de Recherche (senior researcher) at INRIA Saclay Ile-de-France since 2007. After a PhD in pure mathematics, he oriented his research to computational geometry and topology. He is now leading the DataShape team at INRIA, a group working on Topological Data Analysis (TDA), a recent fast growing field at the crossing of mathematics, statistics, machine learning and computer science. Frederic's contributions to the field go from fundamental mathematical aspects to algorithmic and applied problems. He published more than 80 papers in major computer sciences conferences and mathematics journals, he co-authored 2 reference books and 3 patents. He is also an associate editor of 4 international journals. During the last few years Frederic has been heading several national and international research projects on geometric and topological methods in statistics, machine learning and AI. He is also the scientific head of joint industrial research projects between Inria and several companies such as Fujitsu or the French SME Sysnav.