相关论文: Metric Perturbation Resilience

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the…

We study a generalization of $k$-center clustering, first introduced by Kavand et. al., where instead of one set of centers, we have two types of centers, $p$ red and $q$ blue, and where each red center is at least $\alpha$ distant from…

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…

The fair $k$-median problem is one of the important clustering problems. The current best approximation ratio is 4.675 for this problem with 1-fair violation, which was proposed by Bercea et al. [APPROX-RANDOM'2019]. As far as we know,…

We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity…

In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center,…

We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…

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…