54 citations · 227 across the 23 of their papers we have counts for
8 papers · 1 filter
A Structural Average of Labeled Merge Trees for Uncertainty Visualization
Lin Yan, Yusu Wang, Elizabeth Munch +2
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour…
Intrinsic Interleaving Distance for Merge Trees
Ellen Gasparovic, Elizabeth Munch, Steve Oudot +3
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applicat…
Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing
Lin Yan, Yaodong Zhao, Paul Rosen +2
Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data.…
Discrete Stratified Morse Theory: Algorithms and A User's Guide
Kevin Knudson, Bei Wang
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete anal…
Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives
Adam Brown, Bei Wang
In this paper, we investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of strati…
Convergence between Categorical Representations of Reeb Space and Mapper
Elizabeth Munch, Bei Wang
The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientif…
Geometric Inference on Kernel Density Estimates
Jeff M. Phillips, Bei Wang, Yan Zheng
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density esti…
Approximating Local Homology from Samples
Primoz Skraba, Bei Wang
Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sam…