Learning to rank using 1-norm regularization and convex hull reduction

Abstract

The ranking problem appears in many areas of study such as customer rating, social science, economics, and information retrieval. Ranking can be formulated as a classification problem when pair-wise data is considered. However this approach increases the problem complexity from linear to quadratic in terms of sample size. We present in this paper a convex hull reduction method to reduce this impact. We also propose a 1-norm regularization approach to simultaneously find a linear ranking function and to perform feature subset selection. The proposed method is formulated as a linear program. We present experimental results on artificial data and two real data sets, concrete compressive strength data set and Abalone data set.