Related papers: A Global Optimization Algorithm for K-Center Clust…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…
In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center.…
In this paper we consider a generalization of the classical k-center problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The…
We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity…
In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…
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,…
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
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…
The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…
This paper presents an accelerated spherical K-means clustering algorithm for large-scale and high-dimensional sparse document data sets. We design an algorithm working in an architecture-friendly manner (AFM), which is a procedure of…
Clustering analysis has received considerable attention in spatial data mining for several years. With the rapid development of the geospatial information technologies, the size of spatial information data is growing exponentially which…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we…
As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…
We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…
We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster…
Clustering is an unsupervised learning method that constitutes a cornerstone of an intelligent data analysis process. It is used for the exploration of inter-relationships among a collection of patterns, by organizing them into homogeneous…
Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…
In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between…