Factor graph

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A factor graph is an $X, F$ -bipartite graph where $X=\{X_1,X_2,\dots,X_n\}$ is a set of variables and $F=\{f_1,f_2,\dots,f_m\}$ is a set of factors. A factor $f j$ is a function mapping from a subset of variables $X_j\subseteq X$ to some range (such as the real numbers). This graph represents the factorisation

$g(\mathbf{x}) = \prod_{j=1}^m f_j(\mathbf{x_j}),$

where $\mathbf{x}$ is an assignment to all variables in $X$ and $\mathbf{x_j}$ is the assignment of $\mathbf{x}$ to all variables in $X j$ .

[edit] Forney factor graph

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