Left to right: Amartya Banerjee, Aaron Jacobson, Caroline Moosmueller, Shiying Li. Picture from September 2023.

We are interested in developing numerical methods for nonlinear and high-dimensional data analysis. Our focus lies on algorithms that preserve geometric structures, and our work includes optimal transport problems, classification tasks in machine learning, linear and nonlinear approximation, and applications in biology and cancer research.


Caroline Moosmueller
Shiying Li
Amartya Banerjee
Aaron Jacobson
Chuxiangbo Wang
Kwatcho Mahinanda


Computational optimal transport
Approximation theory
Biology and cancer research

  • Paper on Approximation properties of slice-matching operators
    Shiying’s and Caroline’s paper “Approximation properties of slice-matching operators” is available on the arXiv. In this paper we iterative slicing-and-matching schemes, in particular, the approximation power of one step of such schemes. We show an invariance and an equivariance property with respect to global rigid transformations, approximation of the target measure, and derive a connection… Continue reading Paper on Approximation properties of slice-matching operators
  • Paper on stochastic slicing and matching
    A preprint of Shiying’s and Caroline’s paper “Measure transfer via stochastic slicing and matching” is available on the arXiv. In this paper we discuss an iterative slicing-and-matching procedure which can be used for measure approximation. This scheme has first been introduced by PitiĆ© et. al.; we show a convergence proof of a stochastic version.
  • Data science seed grant
    Caroline, together with Shahar Kovalsky, Martin Styner, and Guorong Wu received a seed grant from the School of Data Science and Society at UNC. Our award on “Spatio-temporal analysis of brain functional connectome” will run until June 2024. Official announcement Abstract: We will develop mathematical models and algorithms for the analysis and statistical characterization of… Continue reading Data science seed grant
  • Data Science Networking Event @ UNC
    Happening on April 20, 11:30 am – 1:30 pm at Wilson Library. Caroline will give a 3-minutes flash talk, see here for details.
  • New paper
    Preprint of our new paper “Linearized Wasserstein dimensionality reduction with approximation guarantees” is available on the arXiv. This is joint work with Alex Cloninger, Keaton Hamm, and Varun Khurana.