Related papers: Differentially Private Algorithms for Clustering w…
We consider the problem of clustering in the presence of noise. That is, when on top of cluster structure, the data also contains a subset of \emph{unstructured} points. Our goal is to detect the clusters despite the presence of many…
The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…
We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…
Consider the following problem: given a metric space, some of whose points are "clients", open a set of at most $k$ facilities to minimize the average distance from the clients to these facilities. This is just the well-studied $k$-median…
K-means algorithm is a very popular clustering algorithm which is famous for its simplicity. Distance measure plays a very important rule on the performance of this algorithm. We have different distance measure techniques available. But…
The goal of this paper is to propose and analyze a differentially private randomized mechanism for the $K$-means query. The goal is to ensure that the information received about the cluster-centroids is differentially private. The method…
Differential Privacy (DP) has become a gold standard in privacy-preserving data analysis. While it provides one of the most rigorous notions of privacy, there are many settings where its applicability is limited. Our main contribution is in…
Although numerous clustering algorithms have been developed, many existing methods still leverage k-means technique to detect clusters of data points. However, the performance of k-means heavily depends on the estimation of centers of…
This paper investigates the capability of correctly recovering well-separated clusters by various brands of the $k$-means algorithm. The concept of well-separatedness used here is derived directly from the common definition of clusters,…
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…
In machine learning and data mining, Cluster analysis is one of the most widely used unsupervised learning technique. Philosophy of this algorithm is to find similar data items and group them together based on any distance function in…
Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by…
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly…
We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…
In this paper, we study the individual preference (IP) stability, which is an notion capturing individual fairness and stability in clustering. Within this setting, a clustering is $\alpha$-IP stable when each data point's average distance…
This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…
We revisit the problem of finding a minimum enclosing ball with differential privacy: Given a set of $n$ points in the Euclidean space $\mathbb{R}^d$ and an integer $t\leq n$, the goal is to find a ball of the smallest radius $r_{opt}$…
We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…