Related papers: Using Centroidal Voronoi Tessellations to Scale Up…

Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…

In their recent article (2010), Levy and Liu introduced a generalization of Centroidal Voronoi Tessellation (CVT) - namely the Lp-CVT - that allows the computation of an anisotropic CVT over a sound mathematical framework. In this article a…

High-dimensional images, or images with a high-dimensional attribute vector per pixel, are commonly explored with coordinated views of a low-dimensional embedding of the attribute space and a conventional image representation. Nowadays,…

The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons,…

In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…

Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…

votess is a library for computing parallel 3D Voronoi tessellations on heterogeneous platforms, from CPUs and GPUs, to future accelerator architectures. To do so, it leverages the SYCL abstraction layer to achieve portability and…

We test this premise and explore representation spaces from a single deep convolutional network and their visualization to argue for a novel unified feature extraction framework. The objective is to utilize and re-purpose trained feature…

The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main…

In computer vision tasks, the ability to focus on relevant regions within an image is crucial for improving model performance, particularly when key features are small, subtle, or spatially dispersed. Convolutional neural networks (CNNs)…

Increasing the scalability of machine learning to handle big volume of data is a challenging task. The scale up approach has some limitations. In this paper, we proposed a scale out approach for CNN-ELM based on MapReduce on classifier…

Spatial optimization is often overlooked in many computer vision tasks. Filters should be able to recognize the features of an object regardless of where it is in the image. Similarity search is a crucial task where spatial features decide…

A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…

Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…

We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic…

The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features --…

In this paper, we present a new adaptive feature scaling scheme for ultrahigh-dimensional feature selection on Big Data. To solve this problem effectively, we first reformulate it as a convex semi-infinite programming (SIP) problem and then…

Convolutional Neural Networks have demonstrated superior performance on single image depth estimation in recent years. These works usually use stacked spatial pooling or strided convolution to get high-level information which are common…

Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…