Non-negative matrix factorization has been used as an effective approach for document clustering lately. One advantage of this method is that clustering results can be directly concluded from the factor matrices. This project gives parallel implementation of three algorithms for Non-negative matrix factorization. Experiments of these parallel algorithms for large datasets shows good speedup for...

MOTIVATION Identifying different cancer classes or subclasses with similar morphological appearances presents a challenging problem and has important implication in cancer diagnosis and treatment. Clustering based on gene-expression data has been shown to be a powerful method in cancer class discovery. Non-negative matrix factorization is one such method and was shown to be advantageous over ot...

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by non-negative matrix factorizations. Non-negative matrix factorization represents an emerging example of subspace methods which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing indivi...

We proposed automatic factorization method of biological signals measured by Fluorescence Correlation Spectroscopy (FCS). Since the signals are composed from several positive components, the signals are decomposed by using the idea of Non-negative matrix factorization (NMF). Each component is represented by model functions and the signals are factorized as the non-negative sum of the model func...

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we introduce a new method for collaborative filtering based on Matrix Factorization ...

We prove that the earth mover’s distance problem reduces to a problem with half the number of constraints regardless of the ground distance, and propose a further reduced formulation when the ground distance comes from a graph with a homogeneous neighborhood structure. We also propose to apply our formulation to the non-negative matrix factorization.

Rapid technological advances have led to the production of different types of biological data and enabled construction of complex networks with various types of interactions between diverse biological entities. Standard network data analysis methods were shown to be limited in dealing with such heterogeneous networked data and consequently, new methods for integrative data analyses have been pr...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d ×m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...