Related papers: Elkan's k-Means for Graphs
We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity,…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
We generalise the results of Bhattacharya et al. (Journal of Computing Systems, 62(1):93-115, 2018) for the list-$k$-means problem defined as -- for a (unknown) partition $X_1, ..., X_k$ of the dataset $X \subseteq \mathbb{R}^d$, find a…
This is a survey of the method of graph cuts and its applications to graph clustering of weighted unsigned and signed graphs. I provide a fairly thorough treatment of the method of normalized graph cuts, a deeply original method due to Shi…
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…
We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect…
Mesh partitioning is an indispensable tool for efficient parallel numerical simulations. Its goal is to minimize communication between the processes of a simulation while achieving load balance. Established graph-based partitioning tools…
Motivated by data analysis and machine learning applications, we consider the popular high-dimensional Euclidean $k$-median and $k$-means problems. We propose a new primal-dual algorithm, inspired by the classic algorithm of Jain and…
Clustering is a fundamental unsupervised learning task with applications across a wide range of domains. Popular algorithms such as $k$-means are efficient and widely used, but can be sensitive to outliers, ambiguous boundary points, and…
The input to the $k$-median for lines problem is a set $L$ of $n$ lines in $\mathbb{R}^d$, and the goal is to compute a set of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum of squared distances over every line in $L$ and its…
Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…
Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for…
Context. K-means is a clustering algorithm that has been used to classify large datasets in astronomical databases. It is an unsupervised method, able to cope very different types of problems. Aims. We check whether a variant of the…
The identification of the set of k most central nodes of a graph, or centrality maximization, is a key task in network analysis, with various applications ranging from finding communities in social and biological networks to understanding…
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…
Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…