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Factor graph : ウィキペディア英語版
Factor graph

A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to represent factorization of a probability distribution function, enabling efficient computations, such as the computation of marginal distributions through the sum-product algorithm. One of the important success stories of factor graphs and the sum-product algorithm is the decoding of capacity-approaching error-correcting codes, such as LDPC and turbo codes.
Factor graphs generalize constraint graphs. A factor whose value is either 0 or 1 is called a constraint. A constraint graph is a factor graph where all factors are constraints. The max-product algorithm for factor graphs can be viewed as a generalization of the arc-consistency algorithm for constraint processing.
==Definition==
A factor graph is a bipartite graph representing the factorization of a function. Given a factorization of a function g(X_1,X_2,\dots,X_n),
:g(X_1,X_2,\dots,X_n) = \prod_^m f_j(S_j),
where S_j \subseteq \, the corresponding factor graph G=(X,F,E) consists of variable vertices
X=\, factor vertices F=\, and edges E. The edges depend on the factorization as follows: there is an undirected edge between factor vertex f_j and variable vertex X_k iff X_k \in S_j. The function is tacitly assumed to be real-valued: g(X_1,X_2,\dots,X_n) \in \Bbb .
Factor graphs can be combined with message passing algorithms to efficiently compute certain characteristics of the function g(X_1,X_2,\dots,X_n), such as the marginal distributions.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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