Related papers: PSI: Constructing ad-hoc Simplices to Interpolate …
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
Most existing point cloud upsampling methods have roughly three steps: feature extraction, feature expansion and 3D coordinate prediction. However,they usually suffer from two critical issues: (1)fixed upsampling rate after one-time…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations,…
This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and non-vanishing noise. A generalized least squares estimator is used to estimate the…
In this study, we propose the leveraging of interpretability for tasks beyond purely the purpose of explainability. In particular, this study puts forward a novel strategy for leveraging gradient-based interpretability in the realm of…
We study polynomial approximation on a $d$-cube, where $d$ is large, and compare interpolation on sparse grids, aka Smolyak's algorithm (SA), with a simple least squares method based on randomly generated points (LS) using standard…
We formally introduce a systematic (de/re)-composition approach, based on the algebraic formalism of "Multi-Dimensional Homomorphisms (MDHs)". Our approach is designed as general enough to be applicable to a wide range of data-parallel…
B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs). Unlike pseudo-spectral projection and regression-based stochastic…
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 consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by…
We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…
In the last few years, several methods have been developed to deal with jump singularities in parametric or stochastic hyperbolic PDEs. They typically use some alignment of the jump-sets in physical space before performing well established…
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms…
Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large…