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We interpret non-negative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the positive orthant. We show that under certain conditions, basically requiring that some of the data are spread across the faces of the positive orthant, there is a unique such simplicial… (More)
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S2, the special orthogonal group SO(3), the positive definite matrices SPD(n), and the Grassmann manifolds G(n, k). The representations are based on the deployment of Deslauriers–Dubuc and average-interpolating pyramids “in the… (More)
Scientific computation is emerging as absolutely central to the scientific method. Unfortunately, it's error-prone and currently immature-traditional scientific publication is incapable of finding and rooting out errors in scientific computation-which must be recognized as a crisis. An important recent development and a necessary response to the crisis is… (More)
The classical multivariate linear regression problem assumes p variables X<sub>1</sub>, X<sub>2</sub>,... ,X<sub>p</sub> and a response vector y, each with n observations, and a linear relationship between the two: y = Xbeta + z, where z ~ N(0, sigma<sup>2</sup>). We point out that when p > n, there is a breakdown point for standard model selection… (More)
As computational researchers increasingly make their results available in a reproducible way, and often outside the traditional journal publishing mechanism, questions naturally arise with regard to copyright, subsequent use and citation, and ownership rights in general. The growing number of scientists who release their research publicly face a gap in the… (More)
Rapid release of prepublication data has served the field of genomics well. Attendees at a workshop in Toronto recommend extending the practice to other biological data sets.
This article considers the obstacles involved in creating reproducible computational research as well as some efforts and approaches to overcome them.
BACKGROUND We applied the Virtual Northern technique to human brain mRNA to systematically measure human mRNA transcript lengths on a genome-wide scale. METHODOLOGY/PRINCIPAL FINDINGS We used separation by gel electrophoresis followed by hybridization to cDNA microarrays to measure 8,774 mRNA transcript lengths representing at least 6,238 genes at high… (More)
Science is built upon foundations of theory and experiment validated and improved through open, transparent communication. With the increasingly central role of computation in scientific discovery this means communicating all details of the computations needed for others to replicate the experiment, i.e. making available to others the associated data and… (More)