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...

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

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

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

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

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...

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

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...

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...

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...

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...

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

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...

-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...

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...

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...

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...

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

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...

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

Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those...

but also a clustering coefficient significantly higher than expected by random chance. Watts and Strogatz then proposed a novel graph model, currently...

methods to which randomization and blinding were soon added. An eloquent non-mathematical explanation of the additive effects model was available in 1885...

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

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

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

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...

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...