Matrix factorization or factor analysis is an important task helpful in the analysis of high dimensional real world data. There are several well known methods and algorithms for factorization of real data but many application areas including information retrieval, pattern recognition and data mining often require processing of binary rather than real data. Unfortunately, the methods used for re...

We use a multiscale approach to reduce the time to produce the nonnegative matrix factorization (NMF) of a matrix A, that is, A ≈ WH. We also investigate QR factorization as a method for initializing W during the iterative process for producing the nonnegative matrix factorization of A. Finally, we use our approach to produce nonnegative matrix factorizations for classifying images and compare ...

Recommender system has attracted lots of attentions since it helps users alleviate the information overload problem. Matrix factorization technique is one of the most widely employed collaborative filtering techniques in the research of recommender systems due to its effectiveness and efficiency in dealing with very large user-item rating matrices. Recently, based on the intuition that addition...

Non-negative Matrix Factorization (NMF) is a part-based image representation method which adds a non-negativity constraint to matrix factorization. NMF is compatible with the intuitive notion of combining parts to form a whole face. In this paper, we propose a framework of face recognition by adding NMF constraint and classifier constraints to matrix factorization to get both intuitive features...

This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-ra...

Matrix factorization-based approaches have proven to be efficient for recommender systems. However, due to the time complexity in composing recommendations, matrix factorization-based approaches are inefficient in dealing with large scale datasets. In this paper, we present a new similar user index-based matrix factorization approach for large scale recommender systems. Finding similar users is...

The main aim of this paper is to study quaternion matrix factorization for low-rank completion and its applications in color image processing. For the real-world images, we proposed a novel model called (LRQC), which adds total variation Tikhonov regularization factor matrices preserve spatial/temporal smoothness. Moreover, proximal alternating minimization (PAM) algorithm was tackle correspond...