Related papers: Estimating the persistent homology of $\mathbb{R}^…

We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…

In this paper we give a metric construction of a tree which correctly identifies connected components of superlevel sets of $\mathbb{R}$-valued continuous functions $f$ on $X$ and show that it is possible to retrieve the $H_0$-persistent…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning as shown by Phillips, Wang and Zheng [SoCG 2015]. However, contrary to the case of computing persistent homology…

In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…

We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…

We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval $[a,b]$ into the space of compact non-empty subsets of ${\mathbb R}^d$. All operators are adapted by…

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…

Multiparameter persistent homology is a generalization of classical persistent homology, a central and widely-used methodology from topological data analysis, which takes into account density estimation and is an effective tool for data…

With the aim to improve the performance of feature matching, we present an unsupervised approach to fuse various local descriptors in the space of homographies. Inspired by the observation that the homographies of correct feature…

Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical…

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently…

Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…

Let $X$ be a compact K\"ahler manifold and $\theta$ a smooth closed $(1,1)$-real form representing a big cohomology class $\alpha \in H^{1,1}(X,\R)$. The purpose of this note is to show, using pluripotential and viscosity techniques, that…

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…

Given a random sample from a density function supported on a manifold $M$, a new method for the estimating highest density regions of the underlying population is introduced. The new proposal is based on the empirical version of the opening…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…