Related papers: The computational complexity of some explainable c…

The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…

In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means. When the input is distributed across a large number of machines and the number of…

Explainable clustering by axis-aligned decision trees was introduced by Moshkovitz et al. (2020) and has gained considerable interest. Prior work has focused on minimizing the price of explainability for specific clustering objectives,…

In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…

Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…

Algorithmic solutions have significant potential to improve decision-making across various domains, from healthcare to e-commerce. However, the widespread adoption of these solutions is hindered by a critical challenge: the lack of…

Explainable AI (XAI) is an important developing area but remains relatively understudied for clustering. We propose an explainable-by-design clustering approach that not only finds clusters but also exemplars to explain each cluster. The…

The domain of explainable AI is of interest in all Machine Learning fields, and it is all the more important in clustering, an unsupervised task whose result must be validated by a domain expert. We aim at finding a clustering that has high…

We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…

The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…

$k$-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 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…

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…

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…

Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…

There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results…

In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…

Fair clustering has gained increasing attention in recent years, especially in applications involving socially sensitive attributes. However, existing fair clustering methods often lack interpretability, limiting their applicability in…

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…