Related papers: Cluster Probability in Bootstrap Percolation
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product…
We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core…
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…
The problem of data clustering is one of the most important in data analysis. It can be problematic when dealing with experimental data characterized by measurement uncertainties and errors. Our paper proposes a recursive scheme for…
Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
There is no convincing evidence that backpropagation is a biologically plausible mechanism, and further studies of alternative learning methods are needed. A novel online clustering algorithm is presented that can produce arbitrary shaped…
The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new…
We propose a simple model for periodic clustering of particles under forced oscillation. Effective viscosity is assumed to increase owing to neighboring particles by analogy with the Einstein viscosity law. The linear stability analysis and…
We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
The culling process in Bootstrap Percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap…
Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that…
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the…
Bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of "activation" on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at…
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
It is common when using cross-section or panel data to assign each observation to a cluster and allow for arbitrary patterns of heteroskedasticity and correlation within clusters. For regression models, there are many ways to make…
Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying…
We present conjectures on the scattering terms of cluster scattering diagrams of rank 2, supported by significant computational evidence.