Related papers: Constant Approximation for Individual Preference S…
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…
In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
A common distinction in fair machine learning, in particular in fair classification, is between group fairness and individual fairness. In the context of clustering, group fairness has been studied extensively in recent years; however,…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…
Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation…
Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
We study the design of interactive clustering algorithms for data sets satisfying natural stability assumptions. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable features in many…
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…
Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
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…
Correlation clustering is a ubiquitous paradigm in unsupervised machine learning where addressing unfairness is a major challenge. Motivated by this, we study Fair Correlation Clustering where the data points may belong to different…
A cluster id assignment scheme labels each cluster of a clustering with a distinct id. The goal of id assignment is semantic id stability, which means that, whenever possible, a cluster for the same underlying concept as that of a…
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the…
In this paper, we initiate the study of fair clustering that ensures distributional similarity among similar individuals. In response to improving fairness in machine learning, recent papers have investigated fairness in clustering…
Clustering under most popular objective functions is NP-hard, even to approximate well, and so unlikely to be efficiently solvable in the worst case. Recently, Bilu and Linial \cite{Bilu09} suggested an approach aimed at bypassing this…