相关论文: Greedy k-Center from Noisy Distance Samples

Motivated by the mode estimation problem of an unknown multivariate probability density function, we study the problem of identifying the point with the minimum k-th nearest neighbor distance for a given dataset of n points. We study the…

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to…

The k-means++ algorithm due to Arthur and Vassilvitskii has become the most popular seeding method for Lloyd's algorithm. It samples the first center uniformly at random from the data set and the other $k-1$ centers iteratively according to…

This paper examines the ability of greedy algorithms to estimate a block sparse parameter vector from noisy measurements. In particular, block sparse versions of the orthogonal matching pursuit and thresholding algorithms are analyzed under…

We study the problem of $k$-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm…

In the classical NP-hard metric $k$-median problem, we are given a set of $n$ clients and centers with metric distances between them, along with an integer parameter $k\geq 1$. The objective is to select a subset of $k$ open centers that…

In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a…

We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our…

We study optimization problems in a metric space $(\mathcal{X},d)$ where we can compute distances in two ways: via a ''strong'' oracle that returns exact distances $d(x,y)$, and a ''weak'' oracle that returns distances $\tilde{d}(x,y)$…

In this work we consider the problem of recovering $n$ discrete random variables $x_i\in \{0,\ldots,k-1\}, 1 \leq i \leq n$ (where $k$ is constant) with the smallest possible number of queries to a noisy oracle that returns for a given…

The k-center problem is one of several classic NP-hard clustering questions. For contemporary massive data sets, RAM-based algorithms become impractical. And although there exist good sequential algorithms for k-center, they are not easily…

Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for $k$-clustering (such as $k$-median and $k$-means) assume access to exact pairwise distances -- an unrealistic requirement in many modern…

The Reverse Greedy algorithm (RGreedy) for the k-median problem works as follows. It starts by placing facilities on all nodes. At each step, it removes a facility to minimize the resulting total distance from the customers to the remaining…

In real applications, database systems should be able to manage and process data with uncertainty. Any real dataset may have missing or rounded values, also the values of data may change by time. So, it becomes important to handle these…

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…

The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…