The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netflix ratings.
Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences（俄罗斯科学院马祖克数值数学研究所）；National Research University Higher School of Economics（国立高等经济大学）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
A Subspace Framework for ${\mathcal H}_\infty$-Norm Minimization
Max Planck Institute for Dynamics of Complex Technical Systems（马普复杂技术系统动力学研究所）；Koç University（科奇大学）；Universität Hamburg（汉堡大学）；Technische Universität Berlin（柏林工业大学）
Southeast University（东南大学）；Centre de Recherche en Information Biomédicale Sino-Français (CRIBs)（中法生物医学信息研究中心）；INSERM U 1099（法国国家健康与医学研究院U1099）；Laboratoire Traitement du Signal et de l’Image (LTSI)（信号图像处理实验室）；Université de Rennes 1（雷恩第一大学）
Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization
King Fahd University of Petroleum & Minerals（国王法赫德国王石油与矿产大学）；Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum & Minerals（国王法赫德国王石油与矿产大学智能交通与物流交叉研究中心）
