107 citations · 416 across the 27 of their papers we have counts for
10 papers · 1 filter
Fermat Distance-to-Measure: a robust Fermat-like metric
Jérôme Taupin, Frédéric Chazal
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density ar…
Topological Analysis for Detecting Anomalies (TADA) in Time Series
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…
Topological signatures of periodic-like signals
Wojciech Reise, Bertrand Michel, Frédéric Chazal
We present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local ext…
Optimal quantization of the mean measure and applications to statistical learning
Frédéric Chazal, Clément Levrard, Martin Royer
This paper addresses the case where data come as point sets, or more generally as discrete measures. Our motivation is twofold: first we intend to approximate with a compactly supp…
An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
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. This paper…
Estimating the Reach of a Manifold
Eddie Aamari, Jisu Kim, Frédéric Chazal +3
Various problems in manifold estimation make use of a quantity called the reach, denoted by , which is a measure of the regularity of the manifold. This paper is the first in…