6 papers
A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data
Mary Chriselda Antony Oliver, Kaitlyn Hohmeier, Tuyen Tran +3
High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeat…
Wasserstein Mahalanobis Distances for Recovering Latent Geometry
Chuxiangbo Wang, Shiying Li, Caroline Moosmüller
The Mahalanobis distance is a fundamental covariance-adapted metric for multivariate data and plays a central role in recovering latent geometry from nonlinear observations. We ext…
Persistent Homology for Labeled Datasets: Gromov-Hausdorff Stability and Generalized Landscapes
Yaoying Fu, Evgeniya Lagoda, Shiying Li +3
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spac…
Metric properties of partial and robust Gromov-Wasserstein distances
Jannatul Chhoa, Michael Ivanitskiy, Fushuai Jiang +4
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct m…
Linear optimal transport subspaces for point set classification
Mohammad Shifat E Rabbi, Naqib Sad Pathan, Shiying Li +3
Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is ch…
Approximation properties of slice-matching operators
Shiying Li, Caroline Moosmueller
Iterative slice-matching procedures are efficient schemes for transferring a source measure to a target measure, especially in high dimensions. These schemes have been successfully…