Related papers: Box Filtration

This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial…

Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this…

Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…

We present MonteBoxFinder, a method that, given a noisy input point cloud, fits cuboids to the input scene. Our primary contribution is a discrete optimization algorithm that, from a dense set of initially detected cuboids, is able to…

For numerous reasons there raises a need for dimension reduction that preserves certain characteristics of data. In this work we focus on data coming from a mixture of Gaussian distributions and we propose a method that preserves…

We aim to detect all instances of a category in an image and, for each instance, mark the pixels that belong to it. We call this task Simultaneous Detection and Segmentation (SDS). Unlike classical bounding box detection, SDS requires a…

Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…

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…

We present a new, simple yet effective approach to uplift video object detection. We observe that prior works operate on instance-level feature aggregation that imminently neglects the refined pixel-level representation, resulting in…

Having the right assortment of shipping boxes in the fulfillment warehouse to pack and ship customer's online orders is an indispensable and integral part of nowadays eCommerce business, as it will not only help maintain a profitable…

We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares…

Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…

In this work, we propose a simple but effective channel pruning framework called Progressive Channel Pruning (PCP) to accelerate Convolutional Neural Networks (CNNs). In contrast to the existing channel pruning methods that prune channels…

Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central…

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only…

We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a…

A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…