Factorization and job scheduling: A connection via companion based matrix functions

Tensor Factorization via Matrix Factorization

Tensor factorization arises in many machinelearning applications, such knowledge basemodeling and parameter estimation in latentvariable models. However, numerical meth-ods for tensor factorization have not reachedthe level of maturity of matrix factorizationmethods. In this paper, we propose a newmethod for CP tensor factorization that usesrandom projections to ...

A factorization of the inverse of the shifted companion matrix

Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix

A new fast algorithm for computing the zeros of a polynomial in O(n2) time using O(n) memory is developed. The eigenvalues of the Frobenius companion matrix are computed by applying a nonunitary analogue of Francis’s implicitly shifted QR algorithm to a factored form of the matrix. The algorithm achieves high speed and low memory use by preserving the factored form. It also provides a residual ...

Link Prediction via Matrix Factorization

We propose to solve the link prediction problem in graphs using a supervised matrix factorization approach. The model learns latent features from the topological structure of a (possibly directed) graph, and is shown to make better predictions than popular unsupervised scores. We show how these latent features may be combined with optional explicit features for nodes or edges, which yields bett...

Factorization and Approximation Problems for Matrix Functions

The purpose of this paper is to develop a new approach to certain approximation and factorization problems for matrix-valued functions. The approach is based on studying properties of maximizing vectors of Hankel operators with matrix-valued symbols and on the solution of the so-called recovery problem for unitary-valued matrix functions. In the case of scalar functions such problems were studi...