Related papers: Universal Algorithms for Clustering Problems
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a…
We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…
In the dynamic metric $k$-median problem, we wish to maintain a set of $k$ centers $S \subseteq V$ in an input metric space $(V, d)$ that gets updated via point insertions/deletions, so as to minimize the objective $\sum_{x \in V} \min_{y…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…
Clustering has many important applications in computer science, but real-world datasets often contain outliers. Moreover, the presence of outliers can make the clustering problems to be much more challenging. To reduce the complexities,…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high…
In this paper, we give a conditional lower bound of $n^{\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four,…
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 $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case…
Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information.…
Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…
We study in this paper the problem of maintaining a solution to $k$-median and $k$-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that…
The clustering of data is one of the most important and challenging topics in data science. The minimum sum-of-squares clustering (MSSC) problem asks to cluster the data points into $k$ clusters such that the sum of squared distances…