Search for: All records

ABSTRACT Non‐negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi‐Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts‐based data representations to include mixed‐sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF‐related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new SNF algorithm that utilizes the noise‐insensitive norm. We provide monotonic convergence analysis of the SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed‐sign datasets as well as several randomized mixed‐sign matrices to demonstrate the performance superiority of SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels. 

Abstract The Born–Oppenheimer approximation is the keystone of modern computational chemistry and there is wide interest in understanding under what conditions it remains valid. Hydrogen atom scattering from insulator, semi-metal and metal surfaces has helped provide such information. The approximation is adequate for insulators and for metals it fails, but not severely. Here we present hydrogen atom scattering from a semiconductor surface: Ge(111) c (2 × 8). Experiments show bimodal energy-loss distributions revealing two channels. Molecular dynamics trajectories within the Born–Oppenheimer approximation reproduce one channel quantitatively. The second channel transfers much more energy and is absent in simulations. It grows with hydrogen atom incidence energy and exhibits an energy-loss onset equal to the Ge surface bandgap. This leads us to conclude that hydrogen atom collisions at the surface of a semiconductor are capable of promoting electrons from the valence to the conduction band with high efficiency. Our current understanding fails to explain these observations.