Related papers: On one-dimensional Cluster cluster model
With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the model is supercritical:…
We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have…
The article gives a ring theoretic perspective on cluster algebras. Gei{\ss}-Leclerc-Schr\"oer prove that all cluster variables in a cluster algebra are irreducible elements. Furthermore, they provide two necessary conditions for a cluster…
The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an algebra cluster-concealed in case $T$ is obtained from a…
Until now it has been impossible to observationally measure how star cluster scale height evolves beyond 1Gyr as only small samples have been available. Here we establish a novel method to determine the scale height of a cluster sample…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics which is a special limit of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. The model…
In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
Cluster matching by permuting cluster labels is important in many clustering contexts such as cluster validation and cluster ensemble techniques. The classic approach is to minimize the euclidean distance between two cluster solutions which…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
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…
Using Chandra archival data, we quantify the evolution of cluster morphology with redshift. To quantify cluster morphology, we use the power ratio method developed by Buote and Tsai (1995). Power ratios are constructed from moments of the…
The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the…
We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment…
Galaxy clusters are the largest structures in Universe. They are very important as both cosmological probes and astrophysical laboratories. Several methods have been developed to detect galaxy clusters with different techniques (optical,…