Despite the popularity of density-based clustering, its procedural definition makes it difficult
to analyze compared to clustering methods that minimize a loss function. In this paper, we …

Shortest path graph distances are widely used in data science and machine learning, since
they can approximate the underlying geodesic distance on the data manifold. However, the …

The scattering transform is a multilayered, wavelet-based transform initially introduced as a
model of convolutional neural networks (CNNs) that has played a foundational role in our …

Let $\mathcal {M}\subseteq\mathbb {R}^ d $ denote a low-dimensional manifold and let
$\mathcal {X}=\{x_1,\dots, x_n\} $ be a collection of points uniformly sampled from $\mathcal …

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph
infinity Laplacian Page 1 The Annals of Applied Probability 2024, Vol. 34, No. 4, 3870–3910 …

We analyze the convergence properties of Fermat distances, a family of density-driven
metrics defined on Riemannian manifolds with an associated probability measure. Fermat …

We address the problem of estimating topological features from data in high dimensional
Euclidean spaces under the manifold assumption. Our approach is based on the …

Density-based distances (DBDs) offer an elegant solution to the problem of metric learning.
By defining a Riemannian metric which increases with decreasing probability density …

High-dimensional data arises in numerous applications, and the rapidly developing field of
geometric deep learning seeks to develop neural network architectures to analyze such data …

In this work we study statistical properties of graph-based algorithms for multimanifold
clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a …