3 citations · 10 across the 17 of their papers we have counts for
19 papers
Covariance and Principal Component Analysis on Riemannian Manifolds and Graphs
Luiz Hartmann, Wenwen Li, Washington Mio
We develop notions of covariance and principal component analysis (PCA) for probability measures on Riemannian manifolds of bounded geometry and a discrete counterpart for distribu…
The Observable Wasserstein Distance
Edivaldo Lopes dos Santos, Leandro Vicente Mauri, Washington Mio +1
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed t…
Observable Covariance and Principal Observable Analysis for Data on Metric Spaces
Ece Karacam, Washington Mio, Osman Berat Okutan
Datasets consisting of objects such as shapes, networks, images, or signals overlaid on such geometric objects permeate data science. Such datasets are often equipped with metrics…
Robust Representation and Estimation of Barycenters and Modes of Probability Measures on Metric Spaces
Washington Mio, Tom Needham
This paper is concerned with the problem of defining and estimating statistics for distributions on spaces such as Riemannian manifolds and more general metric spaces. The challeng…
Stability and Approximations for Decorated Reeb Spaces
Justin Curry, Washington Mio, Tom Needham +2
Given a map from a topological space to a metric space , a decorated Reeb space consists of the Reeb space, together with an attribution function whose values re…
On Metrics for Analysis of Functional Data on Geometric Domains
Soheil Anbouhi, Washington Mio, Osman Berat Okutan
This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces,…