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.
A factorgraph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factorgraphs are used to...
In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning...
generalized compressibility factorgraphs based on as many as 25 or more different pure gases, such as the Nelson-Obert graphs. Such graphs are said to have an...
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets...
algebra A von Neumann algebra, with a trivial center Factor (graph theory), a spanning sub graph Any finite contiguous sub-sequence of a word in combinatorics...
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...
constraint satisfaction problem. A constraint graph is a special case of a factorgraph, which allows for the existence of free variables. The constraint hypergraph...
operates on a factorgraph. A factorgraph is a bipartite graph containing nodes corresponding to variables V {\displaystyle V} and factors F {\displaystyle...
BF-graph – Type of directed hypergraph Combinatorial design – Symmetric arrangement of finite sets Factorgraph – A factorgraph is a bipartite graph representing...
mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed...
graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the...
pairs of vertices in the factorgraphs that are either adjacent or identical. The strong product is one of several different graph product operations that...
Bayesian network learning (TBNL) A factorgraph is an undirected bipartite graph connecting variables and factors. Each factor represents a function over the...
length 1), is a connected graph of infinite diameter. For every integer n ≥ 2 {\displaystyle n\geq 2} , the free factorgraph F n ( 1 ) {\displaystyle...
propagation algorithm for clustering and data summarization, and the factorgraph notation for probability models. In the late 1990s, Frey was a leading...
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...
theorem) the graph is chordal (by equivalence to a Bayesian network) When such a factorization does exist, it is possible to construct a factorgraph for the...
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In...
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...
mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful...
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and...