Robust ordinal regression induced by lp -centroid

Ordinal regression (OR) is an important research topic in machine learning and has attracted extensive attention due to its wide applications. So far, a variety of methods have been proposed to perform OR, in which the class-center-induced threshold methods (like KDLOR and MOR) have received more attention, for their simplicity and promising performance. The class-center-induced ORs typically calculate the ordinal thresholds with class centers, which are typically derived from the l(2) -norm. Unfortunately, in such a way, the class means may be biased when the data is corrupted with outliers (i.e., non-i.i.d. noises) such that the resulting OR accuracy will be deteriorated. Motivated by the success of l(p)-norm in applications against noises, in this paper we propose a novel type of class centroid derived from the l(p)-norm (coined as l(p)-centroid) to overcome the drawbacks above, and provide an optimization algorithm and corresponding convergence analysis for computing the l(p)-centroid. To evaluate the effectiveness of l(p)-centroid in OR context against noises, we then combine the l(p)-centroid with two representative class-center-induced ORs, namely discriminant learning based and manifold learning based ORs. Finally, extensive OR experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of the proposed methods to related existing methods. (C) 2018 Elsevier B.V. All rights reserved.