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$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…

The adjusted Rand index (ARI) is commonly used in cluster analysis to measure the degree of agreement between two data partitions. Since its introduction, exploring the situations of extreme agreement and disagreement under different…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its…

In this paper, we investigate mutual information as a cost function for clustering, and show in which cases hard, i.e., deterministic, clusters are optimal. Using convexity properties of mutual information, we show that certain formulations…

We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…

Fairness in clustering has been considered extensively in the past; however, the trade-off between the two objectives -- e.g., can we sacrifice just a little in the quality of the clustering to significantly increase fairness, or…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…

We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…

The Bipartite Polarization Problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labelled graph that represents a debate developed through some social network, where nodes represent…

We study the explainable clustering problem first posed by Moshkovitz, Dasgupta, Rashtchian, and Frost (ICML 2020). The goal of explainable clustering is to fit an axis-aligned decision tree with $K$ leaves and minimal clustering cost…

Diversity maximization problem is a well-studied problem where the goal is to find $k$ diverse items. Fair diversity maximization aims to select a diverse subset of $k$ items from a large dataset, while requiring that each group of items be…

In clustering, strong dominance in the size of a particular cluster is often undesirable, motivating a measure of cluster size uniformity that can be used to filter such partitions. A basic requirement of such a measure is stability:…

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…

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…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with…

We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…

Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…