Related papers: A Simple Deterministic Distributed Low-Diameter Cl…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…
Clustering has become an increasingly important task in analysing huge amounts of data. Traditional applications require that all data has to be located at the site where it is scrutinized. Nowadays, large amounts of heterogeneous, complex…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…
Image segmentation aims at identifying regions of interest within an image, by grouping pixels according to their properties. This task resembles the statistical one of clustering, yet many standard clustering methods fail to meet the basic…
We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these…
We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching…
We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast, linear-time…
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…
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing.…