Related papers: Data analysis and the metric evolution of hypergra…

This paper is the first attempt to use geometric deep learning and Sobolev training to incorporate non-Euclidean microstructural data such that anisotropic hyperelastic material machine learning models can be trained in the finite…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

Geometric data sets arising in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps…

We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. A complex network model gaining considerable popularity builds random…

Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving…

Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis…

In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…

We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…

We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…

Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable…