a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular...

A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to...

partition of the edges of the graph into factors; a k-factorization is a partition into k-factors. For instance a 1-factorization is an edge coloring with...

matching with the factorization labels in turn. Similarly add three more blocks 12CDEF, 34CDEF, and 56CDEF, replacing the factorization labels by the corresponding...

decomposition into as few matchings as possible Graph factorization, a decomposition of a regular graph into regular subgraphs of given degrees Many problems...

the corresponding graphs cannot be decomposed. In this sense, the failure of unique factorization on (possibly disconnected) graphs is akin to the statement...

permutation matrix. A perfect matching is also called a 1-factor; see Graph factorization for an explanation of this term. In some literature, the term complete...

an LDU (factorization with all diagonal entries of L and U equal to 1), then the factorization is unique. In that case, the LU factorization is also unique...

the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution...

of the largest possible number of 1-factorizations. A 1-factorization is a partition of the edge set of the graph into three perfect matchings, or equivalently...

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to...

\nu } . An immediate consequence of the factorization property is that morphisms in a k {\displaystyle k} -graph can be factored in multiple ways: there...

Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and...

discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different...

and that between them include all 5 × 3 = 15 edges of the graph; this graph factorization can be done in 6 different ways. Consider a permutation of...

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

k} -regular graph with 2 n {\displaystyle 2n} vertices is 1-factorable. The perfect 1-factorization conjecture that every complete graph on an even number...

Theorem 2, p. 59, and corollary, p. 65 Tutte, W. T. (1947), "The factorization of linear graphs", The Journal of the London Mathematical Society, 22 (2): 107–111...

"GraphLab: Collaborative filtering library using matrix factorization methods". Archived from the original on 2016-12-20. Retrieved 2016-12-01. "GraphLab:...

algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner...

In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From...

polynomial time algorithm for recognizing tensor product graphs and finding a factorization of any such graph. If either G or H is bipartite, then so is their...

quasi-polynomial time. The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as...

hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two...

form, called factorization is, in general, too difficult to be done by hand-written computation. However, efficient polynomial factorization algorithms...

(LDA), canonical correlation analysis (CCA), or non-negative matrix factorization (NMF) techniques to pre-process the data, followed by clustering via...

Matrix factorization is a class of collaborative filtering algorithms used in recommender systems. Matrix factorization algorithms work by decomposing...

Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography...

theorem) the graph is chordal (by equivalence to a Bayesian network) When such a factorization does exist, it is possible to construct a factor graph for the...

undirected graphs and for directed graphs. In the undirected case a Hamiltonian decomposition can also be described as a 2-factorization of the graph such that...