Related papers: Nonparametric Functional Approximation with Delaun…
Object detection and identification is surely a fundamental topic in the computer vision field; it plays a crucial role in many applications such as object tracking, industrial robots control, image retrieval, etc. We propose a…
Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…
Regression is one of the core problems tackled in supervised learning. Rectified linear unit (ReLU) neural networks generate continuous and piecewise-linear (CPWL) mappings and are the state-of-the-art approach for solving regression…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its…
We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on $\delta$-generic…
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…
We study metrics that assess how close a triangulation is to being a Delaunay triangulation, for use in contexts where a good triangulation is desired but constraints (e.g., maximum degree) prevent the use of the Delaunay triangulation…
Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
Auxiliary tasks facilitate learning in situations where data is scarce or the principal task of interest is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks…
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…
Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods are, however, either parametric or cease to perform well when the data is far from linearly…
Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive…
Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…
Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step…