Related papers: Clustering under Constraints: Efficient Parameteri…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed…
Clustering large spatial databases is an important problem, which tries to find the densely populated regions in a spatial area to be used in data mining, knowledge discovery, or efficient information retrieval. However most algorithms have…
In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…
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…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
We consider the $k$-clustering problem with $\ell_p$-norm cost, which includes $k$-median, $k$-means and $k$-center, under an individual notion of fairness proposed by Jung et al. [2020]: given a set of points $P$ of size $n$, a set of $k$…
Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…
We present a novel framework for concomitant dimension reduction and clustering. This framework is based on a novel class of Bayesian clustering factor models. These models assume a factor model structure where the vectors of common factors…
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…
Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…
We introduce and study the $k$-center clustering problem with set outliers, a natural and practical generalization of the classical $k$-center clustering with outliers. Instead of removing individual data points, our model allows discarding…
The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…