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Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation [1] [2] is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting ...
In mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called a logical matrix . (In some contexts, particularly computer science , the term "Boolean matrix" implies this restriction.)
There exist analogues of the SVD, QR, LU and Cholesky factorizations for quasimatrices and cmatrices or continuous matrices. [13] A ‘quasimatrix’ is, like a matrix, a rectangular scheme whose elements are indexed, but one discrete index is replaced by a continuous index. Likewise, a ‘cmatrix’, is continuous in both indices.
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in combinatorial mathematics and theoretical computer science.
In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as AB = pI , where A and B are square matrices and I is the identity matrix . [ 1 ]
In this matrix representation, each formal concept corresponds to a maximal submatrix (not necessarily contiguous) all of whose elements equal 1. It is however misleading to consider a formal context as boolean, because the negated incidence ("object g does not have attribute m") is not concept forming in the same way as defined above. For this ...
In mathematics, a nonnegative matrix, written , is a matrix in which all the elements are equal to or greater than zero, that is, ,. A positive matrix is a matrix in which all the elements are strictly greater than zero. The set of positive matrices is the interior of the set of all non-negative matrices.
The idea behind matrix factorization is to represent users and items in a lower dimensional latent space. Since the initial work by Funk in 2006 a multitude of matrix factorization approaches have been proposed for recommender systems. Some of the most used and simpler ones are listed in the following sections.