Related papers: Clustering in a hyperbolic model of complex networ…

Clustering of proteins is of interest in cancer cell biology. This article proposes a hierarchical Bayesian model for protein (variable) clustering hinging on correlation structure. Starting from a multivariate normal likelihood, we enforce…

Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…

In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…

We present extended simulations of the distribution of galaxy clusters in different dark matter models, using an optimized version of the Zel'dovich approximation. Six different dark matter models are studied: Standard CDM, Open CDM, Tilted…

The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…

Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…

Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the…

This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the…

Let $k,d $ be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a $d$-dimensional Poisson Boolean model with balls of fixed radius is of order $k$, as the…

We develop a unified approach to the problem of clustering in the three different fields of applications, as indicated in the title the paper. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fawler…

We use very large cosmological N--body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM)…

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…

We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and…

The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete…

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…