Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...

In this paper, we consider the symbolic factorization step in computing the Cholesky factorization of a sparse symmetric positive definite matrix on distributedmemory multiprocessor systems. By exploiting the supernodal structure in the Cholesky factor, the performance of a previous parallel symbolic factorization algorithm is improved. Empirical tests demonstrate that there can be drastic redu...

Air pollution associated with atmospheric fine particulate matter (PM2.5, i.e., particles with an aerodynamic diameter of 2.5mm or less) is a serious problem in Beijing, China. To provide a better understanding of the sources contributing to PM2.5, 24-h samples were collected at 6-day intervals in January, April, July, and October in 2000 at five locations in the Beijing metropolitan area. Both...

Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A ≈ RTR up to any desired accuracy, where R is an upper triangular hierarchically semiseparable (HSS) matrix. The factorization is stable, robust, and efficient. The method compresses off-diagonal blocks with rank-revealing orthogonal decompositions. In the meantime, positive semidefinite te...

Atmospheric Chemistry and Physics Discussions This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available. Abstract The goal of this research is to quantify diesel-and gasoline-powered motor vehicle emissions within the Mexico City Metropolitan Area (MCMA) using on-road measurements cap...

Traditional Collaborative Filtering algorithms for recommendation are designed for stationary data. Likewise, conventional evaluation methodologies are only applicable in offline experiments, where data and models are static. However, in real world systems, user feedback is continuously being generated, at unpredictable rates. One way to deal with this data stream is to perform online model upd...

Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...

Given a sparse symmetric positive definite matrix AAT and an associated sparse Cholesky factorization LDLT or LLT, we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis and manipulation of the underlying graph structure and on ideas of Gill et al. [Math. Comp., 28 (1974), ...

This paper presents a suucient condition on sparsity patterns for the existence of the incomplete Cholesky factorization. Given the sparsity pattern P(A) of a matrix A, and a target sparsity pattern P satisfying the condition, incomplete Cholesky factorization successfully completes for all symmetric positive deenite matrices with the same pattern P(A). This condition is also necessary in the s...

This paper presents a su cient condition on sparsity patterns for the existence of the incomplete Cholesky factorization. Given the sparsity pattern P (A) of a matrix A, and a target sparsity pattern P satisfying the condition, incomplete Cholesky factorization successfully completes for all symmetric positive de nite matrices with the same pattern P (A). It is also shown that this condition is...