random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial...

Random cluster model Critical three-state Potts model Chiral Potts model Square-lattice Ising model Minimal models Z N model Cellular Potts model Wu...

information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused...

and Gaussian mixture modeling. They both use cluster centers to model the data; however, k-means clustering tends to find clusters of comparable spatial...

introduced as the Fortuin–Kasteleyn random cluster model, which has many connections with the Ising model and other Potts models. Bernoulli (bond) percolation...

The key ingredient was the random cluster model, a representation of the Ising or Potts model through percolation models of connecting bonds, due to...

(also known as co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes. Group models: some algorithms...

into these groups (known as clusters) and a simple random sample of the groups is selected. The elements in each cluster are then sampled. If all elements...

polynomial, Tutte’s own dichromatic polynomial and Fortuin–Kasteleyn’s random cluster model under simple transformations. It is essentially a generating function...

event are negatively correlated. It was obtained by studying the random cluster model. An earlier version, for the special case of i.i.d. variables, called...

model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering....

Hugo (2012-08-01). "The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1". Probability Theory and Related Fields. 153...

(}|x|+|1-x|+1{\Big )}} The Ising model has a description as a random cluster model due to Fortuin and Kasteleyn. In this description...

context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph...

Hugo (18 March 2011). "The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1 {\displaystyle q\geq 1} " (PDF). Probability...

-state Potts model or critical random cluster model is a conformal field theory that generalizes and unifies the critical Ising model, Potts model, and percolation...

mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are...

violated, the random-effect must be modeled explicitly in the fixed part of the model, either by using dummy variables or including cluster means of all...

Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named...

ISBN 9781482204964. Grimmett, Geoffrey (2006). "Random-Cluster Measures". The Random-Cluster Model. Grundlehren der Mathematischen Wissenschaften. Vol...

Block randomization Systematic randomization Cluster randomization Multistage sampling Quasi-randomization Covariate Adaptive Randomization Randomized algorithm...

reproduces the cluster size distribution and freezing properties of k-SAT and k-COL in the large-k limit. This is similar to how the random energy model is the...

city. Cluster sampling (also known as clustered sampling) generally increases the variability of sample estimates above that of simple random sampling...

accurately-modeled autocorrelation, clustered standard errors are consistent in the presence of cluster-based sampling or treatment assignment. Clustered standard...

algorithm. In a series of papers with C. M. Fortuin he developed random cluster model and obtained the FKG inequality. For Bernoulli percolation on graphs...

graph expresses the conditional dependence structure between random variables. Graphical models are commonly used in probability theory, statistics—particularly...

clustering coefficient as a function of the degree of the node, in hierarchical models nodes with more links are expected to have a lower clustering coefficient...

be obtained by Monte Carlo simulation. A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps...

modules that do not have singular vectors, for example in the critical random cluster model. For any c , h ∈ C {\displaystyle c,h\in \mathbb {C} } , the involution...

the model is closely related to the random cluster model, which can also be formulated in terms of non-crossing loops. Much less is known in models where...