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Found 16 papers, 8 papers with code
Choosing the parameter of the Fermat distance: navigating geometry and noise
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.
MAGDiff: Covariate Data Set Shift Detection via Activation Graphs of Deep Neural Networks
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.
RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds
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.
Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs
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.
Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
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.
ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning
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.
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
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.
DTM-based Filtrations
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
An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
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.
Data driven estimation of Laplace-Beltrami operator
Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning.
Robust Topological Inference: Distance To a Measure and Kernel Distance
However, the empirical distance function is highly non-robust to noise and outliers.
Statistics Theory Computational Geometry Algebraic Topology Statistics Theory
Subsampling Methods for Persistent Homology
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
Stochastic Convergence of Persistence Landscapes and Silhouettes
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
On the Bootstrap for Persistence Diagrams and Landscapes
Persistent homology probes topological properties from point clouds and functions.
Algebraic Topology Computational Geometry Applications
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
In this paper, we study topological persistence in general metric spaces, with a statistical approach.
Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs.
