Related papers: k-d Darts: Sampling by k-Dimensional Flat Searches
We present a new deep learning architecture (called Kd-network) that is designed for 3D model recognition tasks and works with unstructured point clouds. The new architecture performs multiplicative transformations and share parameters of…
Clustering large amount of data is becoming increasingly important in the current times. Due to the large sizes of data, clustering algorithm often take too much time. Sampling this data before clustering is commonly used to reduce this…
A k-dissimilarity map on a finite set X is a function D : X \choose k \rightarrow R assigning a real value to each subset of X with cardinality k, k \geq 2. Such functions, also sometimes known as k-way dissimilarities, k-way distances, or…
We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we…
This paper proposes an efficient data structure, ikd-Tree, for dynamic space partition. The ikd-Tree incrementally updates a k-d tree with new coming points only, leading to much lower computation time than existing static k-d trees.…
State-of-the-art results in deep learning have been improving steadily, in good part due to the use of larger models. However, widespread use is constrained by device hardware limitations, resulting in a substantial performance gap between…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generalized Diversity Subsampling (g-DS) algorithm, to select a subsample following some target probability distribution from a finite data set and demonstrates its…
We consider the well-studied Sparse Fourier transform problem, where one aims to quickly recover an approximately Fourier $k$-sparse vector $\widehat{x} \in \mathbb{C}^{n^d}$ from observing its time domain representation $x$. In the exact…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…
Knowledge distillation (KD) is an effective method for compressing models in object detection tasks. Due to limited computational capability, UAV-based object detection (UAV-OD) widely adopt the KD technique to obtain lightweight detectors.…
Accurate, high-resolution, and real-time DOA estimation is a cornerstone of environmental perception in automotive radar systems. While sparse signal recovery techniques offer super-resolution and high-precision estimation, their…
Data mining has traditionally focused on the task of drawing inferences from large datasets. However, many scientific and engineering domains, such as fluid dynamics and aircraft design, are characterized by scarce data, due to the expense…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…
The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point…