no code implementations • 10 Jun 2024 • Frédéric Chazal, Martin Royer, Clément Levrard

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels.

no code implementations • 30 Nov 2023 • Frédéric Chazal, Laure Ferraris, Pablo Groisman, Matthieu Jonckheere, Frédéric Pascal, Facundo Sapienza

The Fermat distance has been recently established as a useful tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploding the geometrical and statistical properties of the dataset.

1 code implementation • 22 May 2023 • Charles Arnal, Felix Hensel, Mathieu Carrière, Théo Lacombe, Hiroaki Kurihara, Yuichi Ike, Frédéric Chazal

Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their performance can be severely impacted by differences in distribution between the data on which they were trained and that on which they are deployed.

1 code implementation • 3 Feb 2022 • Thibault de Surrel, Felix Hensel, Mathieu Carrière, Théo Lacombe, Yuichi Ike, Hiroaki Kurihara, Marc Glisse, Frédéric Chazal

The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains.

no code implementations • 7 May 2021 • Théo Lacombe, Yuichi Ike, Mathieu Carriere, Frédéric Chazal, Marc Glisse, Yuhei Umeda

We showcase experimentally the potential of Topological Uncertainty in the context of trained network selection, Out-Of-Distribution detection, and shift-detection, both on synthetic and real datasets of images and graphs.

1 code implementation • 14 Oct 2019 • Quentin Mérigot, Alex Delalande, Frédéric Chazal

This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density.

no code implementations • 30 Sep 2019 • Martin Royer, Frédéric Chazal, Clément Levrard, Umeda Yuhei, Ike Yuichi

Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks.

1 code implementation • 20 Apr 2019 • Mathieu Carrière, Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer, Yuhei Umeda

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science.

2 code implementations • 12 Nov 2018 • Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, Yuhei Umeda

Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e. g. the Cech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.

Computational Geometry Algebraic Topology

1 code implementation • 11 Oct 2017 • Frédéric Chazal, Bertrand Michel

Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data.

no code implementations • NeurIPS 2016 • Frédéric Chazal, Ilaria Giulini, Bertrand Michel

Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning.

2 code implementations • 22 Dec 2014 • Frédéric Chazal, Brittany T. Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, Larry Wasserman

However, the empirical distance function is highly non-robust to noise and outliers.

Statistics Theory Computational Geometry Algebraic Topology Statistics Theory

no code implementations • 7 Jun 2014 • Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, Larry Wasserman

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.

Algebraic Topology Computational Geometry Applications

no code implementations • 2 Dec 2013 • Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram.

Statistics Theory Computational Geometry Algebraic Topology Statistics Theory

1 code implementation • 2 Nov 2013 • Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, Larry Wasserman

Persistent homology probes topological properties from point clouds and functions.

Algebraic Topology Computational Geometry Applications

no code implementations • 27 May 2013 • Frédéric Chazal, Marc Glisse, Catherine Labruère, Bertrand Michel

In this paper, we study topological persistence in general metric spaces, with a statistical approach.

no code implementations • 6 May 2013 • Frédéric Chazal, Jian Sun

In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs.

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