We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...

We present a novel strategy for sparse direct factorizations that is geared towards the matrices that arise from hp-adaptive Finite Element Methods. In that context, a sequence of linear systems derived by successive local refinement of the problem domain needs to be solved. Thus, there is an opportunity for a factorization strategy that proceeds by updating (and possibly downdating) the factor...

Routines exist in LAPACK for computing the Cholesky factorization of a symmetric positive definite matrix and in LINPACK there is a pivoted routine for positive semidefinite matrices. We present new higher level BLAS LAPACK-style codes for computing this pivoted factorization. We show that these can be many times faster than the LINPACK code. Also, with a new stopping criterion, there is more r...

Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...

Abstract—What matrix factorization methods do is reduce the dimensionality of data without losing any important information. In this work, we present Non-negative Matrix Factorization (NMF) method, focusing on its advantages concerning other factorization. We discuss main optimization algorithms, used to solve NMF problem, and their convergence. The paper also contains a comparative study betwe...

Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian...

Motivated by an application in computational biology, we consider low-rank matrix factorization with {0, 1}-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size 2m·r, where m is the dimension of the data p...

We discuss partitioning methods using hypergraphs to produce fill-reducing orderings of sparse matrices for Cholesky, LU and QR factorizations. For the Cholesky factorization, we investigate a recent result on pattern-wise decomposition of sparse matrices, generalize the result, and develop algorithmic tools to obtain more effective ordering methods. The generalized results help us to develop f...

In this paper, we propose a Weakly Supervised Matrix Factorization (WSMF) approach to the problem of image parsing with noisy tags, i.e., segmenting noisily tagged images and then classifying the regions only with image-level labels. Instead of requiring clean but expensive pixel-level labels as strong supervision in the traditional image parsing methods, we take noisy image-level labels as wea...

Matrix factorization has now become a dominant solution for personalized recommendation on the Social Web. To alleviate the cold start problem, previous approaches have incorporated various additional sources of information into traditional matrix factorization models. These upgraded models, however, achieve only “marginal” enhancements on the performance of personalized recommendation. Therefo...