Related papers: Clustering and the hyperbolic geometry of complex …
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
Mode-based clustering methods define clusters to be the basins of attraction of the modes of a density estimate. The most common version is mean shift clus- tering which uses a gradient ascent algorithm to find the basins. Rodriguez and…
Clustering is one of the most complex phenomena known to the structure of atomic nuclei. A comprehensive description of this ubiquitous phenomenon goes beyond standard shell model and cluster model frameworks. We argue that clustering is a…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering methods have…
Recent empirical work [Leskovec2009] has suggested the existence of a size threshold for the existence of clusters within many real-world networks. We give the first proof that this clustering size threshold exists within a real-world…
Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
The idea of representations of the data in negatively curved manifolds recently attracted a lot of attention and gave a rise to the new research direction named {\it hyperbolic machine learning} (ML). In order to unveil the full potential…
The Holme-Kim random graph processes is a variant of the Barabasi-Albert scale-free graph that was designed to exhibit clustering. In this paper we show that whether the model does indeed exhibit clustering depends on how we define the…
Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the…
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…