Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Hickok, Abigail"'
We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning: we show that when the data g
Externí odkaz:
http://arxiv.org/abs/2410.01149
Autor:
Arya, Shreya, Giunti, Barbara, Hickok, Abigail, Kanari, Lida, McGuire, Sarah, Turner, Katharine
In this paper, we study the geometric decomposition of the degree-$0$ Persistent Homology Transform (PHT) as viewed as a persistence diagram bundle. We focus on star-shaped objects as they can be segmented into smaller, simpler regions known as ``sec
Externí odkaz:
http://arxiv.org/abs/2408.14995
Autor:
Hickok, Abigail, Blumberg, Andrew J.
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the estimator is con
Externí odkaz:
http://arxiv.org/abs/2308.02615
Autor:
Hickok, Abigail
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space $B$. In this paper, we present an algorithm for computing piecewis
Externí odkaz:
http://arxiv.org/abs/2210.06424
Autor:
Hickok, Abigail
I introduce the concept of a persistence diagram (PD) bundle, which is the space of PDs for a fibered filtration function (a set $\{f_p: \mathcal{K}^p \to \mathbb{R}\}_{p \in B}$ of filtrations that is parameterized by a topological space $B$). Speci
Externí odkaz:
http://arxiv.org/abs/2210.05124
It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability
Externí odkaz:
http://arxiv.org/abs/2206.04834
Autor:
Hickok, Abigail
We develop novel methods for using persistent homology to infer the homology of an unknown Riemannian manifold $(M, g)$ from a point cloud sampled from an arbitrary smooth probability density function. Standard distance-based filtered complexes, such
Externí odkaz:
http://arxiv.org/abs/2112.03334
We develop a method for analyzing spatial and spatiotemporal anomalies in geospatial data using topological data analysis (TDA). To do this, we use persistent homology (PH), which allows one to algorithmically detect geometric voids in a data set and
Externí odkaz:
http://arxiv.org/abs/2107.09188
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases stud
Externí odkaz:
http://arxiv.org/abs/2104.00720
People's opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social i
Externí odkaz:
http://arxiv.org/abs/2102.06825