Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametr...

NIMFA is an open-source Python library that provides a unified interface to nonnegative matrix factorization algorithms. It includes implementations of state-of-the-art factorization methods, initialization approaches, and quality scoring. It supports both dense and sparse matrix representation. NIMFA’s component-based implementation and hierarchical design should help the users to employ alrea...

We discuss factorization in heavy quarkonium production in high energy collisions using NRQCD. Infrared divergences at NNLO are not matched by conventional NRQCD matrix elements. However, we show that gauge invariance and factorization require that conventional NRQCD production matrix elements be modified to include Wilson lines or non-abelian gauge links. With this modification NRQCD factoriza...

The generalized Cholesky factorization and the Cholesky-like factorization are two generalizations of the classic Cholesky factorization. In this paper, the rigorous multiplicative perturbation bounds for the two factorizations are derived using the matrix equation and the refined matrix equation approaches. The corresponding first-order multiplicative perturbation bounds, as special cases, are...

This is a concise survey of some results and open problems concerning Wiener-Hopf factorization and almost periodic factorization of matrix functions. Several classes of discontinuous matrix functions are considered. Also sketched is the abstract framework which unifies the two types of factorization. Mathematics Subject Classification (2010). Primary 47A68; Secondary 30E25, 43A75, 45F15, 47B35 .

This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A, ..., A} and {B, ..., B} such that Xi,j = trace(AB) for i = 1, ...,m, and ...

Generally, data mining in larger datasets consists of certain limitations in identifying the relevant datasets for the given queries. The limitations include: lack of interaction in the required objective space, inability to handle the data sets or discrete variables in datasets, especially in the presence of missing variables and inability to classify the records as per the given query, and fi...

In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.

Design of recommender system following the latent factor model is widely cast as a matrix factorization problem yielding a rating matrix, which is a product of a dense user and a dense item factor matrices. A dense user factor matrix is a credible assumption as all users are expected to have some degree of affinity towards all the latent factors. However, for items it’s not a reasonable supposi...

Many unsupervised learning problems can be expressed as a form of matrix factorization, reconstructing an observed data matrix as the product of two matrices of latent variables. A standard challenge in solving these problems is determining the dimensionality of the latent matrices. Nonparametric Bayesian matrix factorization is one way of dealing with this challenge, yielding a posterior distr...