Related papers: Manifold Density Estimation via Generalized Dequan…
Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature…
We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood…
Experimental data in particle and nuclear physics, particle astrophysics, and radiation protection dosimetry are collected using experimental facilities that consist of a complex system of sensors, electronics, and software. Measured…
Given a sample of an abstract manifold immersed in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its tangent bundle -- seen as subset of another Euclidean space…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
In the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…
We define and study a family of distributions with domain complete Riemannian manifold. They are obtained by projection onto a fixed tangent space via the inverse exponential map. This construction is a popular choice in the literature for…
In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…
Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model,…
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in $\Lambda$CDM N-body simulations. This function is universal across void size and redshift, accurately…