Expectile Matrix Factorization for Skewed Data Analysis

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose \emph{expectile matrix factorization} by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.Comment: 8 page main text with 5 page supplementary documents, published in AAAI 201

Growth of Large Domain Epitaxial Graphene on the C-Face of SiC

Growth of epitaxial graphene on the C-face of SiC has been investigated. Using a confinement controlled sublimation (CCS) method, we have achieved well controlled growth and been able to observe propagation of uniform monolayer graphene. Surface patterns uncover two important aspects of the growth, i.e. carbon diffusion and stoichiometric requirement. Moreover, a new "stepdown" growth mode has been discovered. Via this mode, monolayer graphene domains can have an area of hundreds of square micrometers, while, most importantly, step bunching is avoided and the initial uniformly stepped SiC surface is preserved. The stepdown growth provides a possible route towards uniform epitaxial graphene in wafer size without compromising the initial flat surface morphology of SiC.Comment: 18 pages, 8 figure