Related papers: Nearest Neighbor Sampling of Point Sets using Rays

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets,…

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…

We introduce a new approach for applying sampling-based sketches to two and three mode tensors. We illustrate our technique to construct sketches for the classical problems of $\ell_0$ sampling and producing $\ell_1$ embeddings. In both…

We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these…

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…

Most previous bounding-box-based segmentation methods assume the bounding box tightly covers the object of interest. However it is common that a rectangle input could be too large or too small. In this paper, we propose a novel segmentation…

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…

Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the…

Recently proposed neural network architectures like PointNet [QSMG16] and PointNet++ [QYSG17] have made it possible to apply Deep Learning to 3D point sets. The feature representations of shapes learned by these two networks enabled…

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…

Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with…

With the rapid growing of remotely sensed imagery data, there is a high demand for effective and efficient image retrieval tools to manage and exploit such data. In this letter, we present a novel content-based remote sensing image…

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$…

Local graph neighborhood sampling is a fundamental computational problem that is at the heart of algorithms for node representation learning. Several works have presented algorithms for learning discrete node embeddings where graph nodes…

We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points…

Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…

Indoor localization is a supporting technology for a broadening range of pervasive wireless applications. One promis- ing approach is to locate users with radio frequency fingerprints. However, its wide adoption in real-world systems is…