• Corpus ID: 251442627

Universal Mappings and Analysis of Functional Data on Geometric Domains

@inproceedings{Anbouhi2022UniversalMA,
  title={Universal Mappings and Analysis of Functional Data on Geometric Domains},
  author={Soheil Anbouhi and Washington Mio and Osman Berat Okutan},
  year={2022}
}
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, which we refer to as fields. Formally, fields are viewed as 1-Lipschitz mappings between Polish spaces, with the domain possibly equipped with a probability measure. We establish the existence and uniqueness, up to isometry, of Urysohn fields; that is, universal and homogeneous elements for this class. We prove a… 

References

SHOWING 1-10 OF 26 REFERENCES

Gromov–Wasserstein Distances and the Metric Approach to Object Matching

  • F. Mémoli
  • Computer Science
    Found. Comput. Math.
  • 2011
This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff distance which have the goal of modeling and tackling the practical problems of object matching and comparison by proving explicit lower bounds for the proposed distance that involve many of the invariants previously reported by researchers.

Random and Universal Metric Spaces

We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone ℛℛ of distance matrices, and consider geometric and probabilistic problems connected with this object. The

A topological study of functional data and Fréchet functions of metric measure spaces

This work studies the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces and investigates the stability of these invariants using metrics that downplay regions where signals are weak.

Convergence of probability measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the

Geometry in Urysohn's universal metric space

Optimal Transport: Old and New

Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical

Fused Gromov-Wasserstein Distance for Structured Objects

The mathematical framework for the Fused Gromov-Wasserstein distance is provided, its metric and interpolation properties are proved, and a concentration result for the convergence of finite samples is provided.

Probability distribution of metric measure spaces

Universal and ultrahomogeneous Polish metric structures

We use Fra\" iss\'e theoretic methods to construct several universal and ultrahomogeneous Polish metric structures. Namely, universal and ultrahomogeneous Polish metric space equipped with countably

Real Analysis and Probability

1. Foundations: set theory 2. General topology 3. Measures 4. Integration 5. Lp spaces: introduction to functional analysis 6. Convex sets and duality of normed spaces 7. Measure, topology, and