In statistical mechanics, probability theory, graph theory, etc. the 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 structures, electrical networks, etc.[1][2] It is also referred to as the RC model or sometimes the FK representation after its founders Cees Fortuin and Piet Kasteleyn.[3]
^Fortuin; Kasteleyn (1972). "On the random-cluster model: I. Introduction and relation to other models". Physica. 57 (4): 536. Bibcode:1972Phy....57..536F. doi:10.1016/0031-8914(72)90045-6.
^Newman, Charles M. (1994), Grimmett, Geoffrey (ed.), "Disordered Ising Systems and Random Cluster Representations", Probability and Phase Transition, NATO ASI Series, Dordrecht: Springer Netherlands, pp. 247–260, doi:10.1007/978-94-015-8326-8_15, ISBN 978-94-015-8326-8, retrieved 2021-04-18
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randomclustermodel is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial...
introduced as the Fortuin–Kasteleyn randomclustermodel, which has many connections with the Ising model and other Potts models. Bernoulli (bond) percolation...
information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused...
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 randomclustermodel under simple transformations. It is essentially a generating function...
(also known as co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes. Group models: some algorithms...
Hugo (2012-08-01). "The self-dual point of the two-dimensional random-clustermodel is critical for q ≥ 1". Probability Theory and Related Fields. 153...
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a...
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...
Multilevel models (also known as hierarchical linear models, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects...
event are negatively correlated. It was obtained by studying the randomclustermodel. An earlier version, for the special case of i.i.d. variables, called...
mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are...
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...
sampling method should be distinguished from cluster sampling, where a simple random sample of several entire clusters is selected to represent the whole population...
methods to which randomization and blinding were soon added. An eloquent non-mathematical explanation of the additive effects model was available in 1885...
hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies...
the Database of Surnames in The Netherlands C.M. Fortuin, On the random-clustermodel, PhD dissertation with Pieter Kasteleyn, Leiden, 1971 This page lists...
this model to work without pre-specifying a fixed number of clusters K {\displaystyle K} . Mathematically, this means we would like to select a random prior...
edges. Random field techniques A Markov random field, also known as a Markov network, is a model over an undirected graph. A graphical model with many...
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