Companion based matrix functions: Description and minimal factorization

A factorization of the inverse of the shifted companion matrix

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...

Feature-Based Matrix Factorization

Recommender system has been more and more popular and widely used in many applications recently. The increasing information available, not only in quantities but also in types, leads to a big challenge for recommender system that how to leverage these rich information to get a better performance. Most traditional approaches try to design a specific model for each scenario, which demands great e...

Symmetry-based matrix factorization

We present a method to factor a given matrix M into a short product of sparse matrices, provided M has a suitable “symmetry”. This sparse factorization represents a fast algorithm for the matrix-vector multiplication with M . The factorization method consists of two essential steps. First, a combinatorial search is used to compute a suitable symmetry of M in the form of a pair of group represen...

Coupled Item-Based Matrix Factorization

The essence of the challenges cold start and sparsity in Recommender Systems (RS) is that the extant techniques, such as Collaborative Filtering (CF) and Matrix Factorization (MF), mainly rely on the user-item rating matrix, which sometimes is not informative enough for predicting recommendations. To solve these challenges, the objective item attributes are incorporated as complementary informa...