Related papers: Regularity in the distribution of superclusters

We develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to…

We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…

Several works have shown that the regularization mechanisms underlying deep neural networks' generalization performances are still poorly understood. In this paper, we hypothesize that deep neural networks are regularized through their…

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

We will use the factors obtained by correspondence analysis to find biclustering of a contingency table such that the row-column cluster pairs are regular, i.e., they have small discrepancy. In our main theorem, the constant of the…

There are many cluster analysis methods that can produce quite different clusterings on the same dataset. Cluster validation is about the evaluation of the quality of a clustering; "relative cluster validation" is about using such criteria…

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…

When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…

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…

The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…

Galaxies are not uniformly distributed in space. On large scales the Universe displays coherent structure, with galaxies residing in groups and clusters on scales of ~1-3 Mpc/h, which lie at the intersections of long filaments of galaxies…

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…