Ranking from Crowdsourced Pairwise Comparisons via Smoothed Matrix Manifold Optimization

摘要: As the blooming development of data mining in social computing systems (e.g., crowdsourcing system), statistical inference from crowdsourced severs as a powerful tool to provide diversified services. To support critical applications recommendation), this paper, we shall focus on collaborative ranking problems and construct system which input is pairwise comparisons output individual rankings. Under Bradley-Terry-Luce (BTL) parametric model assumption, present maximum likelihood estimation (MLE) based low-rank approach estimate underlying weight/score matrix, thereby predicting for each user. address unique challenge coupled non-convex constraint non-smooth elementwise infinity norm resulting MLE problem, propose novel regularized formulation with smoothed surrogate norm. By further exploiting geometry quotient manifolds fixed-rank matrices, solve rank-constrained optimization problem via developing Riemannian trust-region algorithm converges an approximate local minimum arbitrary initial points. Numerical results demonstrate extraordinary effectiveness proposed method compared state-of-art algorithms.