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...

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...

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...

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

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

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...

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

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...

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

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...

Multilevel models (also known as hierarchical linear models, linear mixed-effect models, mixed models, nested data models, random coefficient, random-effects...

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

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...

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...

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...

Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude...

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

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...

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...

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...

sampling method should be distinguished from cluster sampling, where a simple random sample of several entire clusters is selected to represent the whole population...

original dataset. A diffusion model models data as generated by a diffusion process, whereby a new datum performs a random walk with drift through the space...

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...

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured...

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

the Database of Surnames in The Netherlands C.M. Fortuin, On the random-cluster model, PhD dissertation with Pieter Kasteleyn, Leiden, 1971 This page lists...