Related papers: Nonparametric, data-based kernel interpolation for…
Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…
Feature preprocessing continues to play a critical role when applying machine learning and statistical methods to tabular data. In this paper, we propose the use of the kernel density integral transformation as a feature preprocessing step.…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel…
This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a system of partial differential equations (PDEs) can…
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…
Object tracking is a fundamental task in computer vision, requiring the localization of objects of interest across video frames. Diffusion models have shown remarkable capabilities in visual generation, making them well-suited for…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
We present a data-driven approach to mathematically model physical systems whose governing partial differential equations are unknown, by learning their associated Green's function. The subject systems are observed by collecting…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
Point clouds are unstructured and unordered data, as opposed to images. Thus, most machine learning approach developed for image cannot be directly transferred to point clouds. In this paper, we propose a generalization of discrete…