Dist2Cycle: A Simplicial Neural Network for Homology Localization

1 code implementation • 28 Oct 2021 • Alexandros Dimitrios Keros, Vidit Nanda, Kartic Subr

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once.

Tangent Space and Dimension Estimation with the Wasserstein Distance

no code implementations • 12 Oct 2021 • Uzu Lim, Harald Oberhauser, Vidit Nanda

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space.

Geometric anomaly detection in data

1 code implementation • 25 Aug 2019 • Bernadette J. Stolz, Jared Tanner, Heather A. Harrington, Vidit Nanda

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data.

Algebraic Topology Algebraic Geometry 57N80

Persistence paths and signature features in topological data analysis

no code implementations • 1 Jun 2018 • Ilya Chevyrev, Vidit Nanda, Harald Oberhauser

We introduce a new feature map for barcodes that arise in persistent homology computation.

General Classification Topological Data Analysis

Discrete Morse theory for computing cellular sheaf cohomology

1 code implementation • 23 Dec 2013 • Justin Curry, Robert Ghrist, Vidit Nanda

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology.

Algebraic Topology 55-04