Ordinal regression (OR) is a learning paradigm lying between classification and regression and has been attracting increasing attention in recent years due to its wide applications such as human age estimation. To date, there have been a variety of methods proposed for OR, among which the category of threshold-based OR becomes one of the representatives with preferable performance. Typical threshold-based methods, such as discriminant learning for OR (i.e., KDLOR), OR via manifold learning (i.e., MOR), usually seek an OR projection direction along which to maximally separate classes by a sequence of ordinal thresholds. Although having yielded encouraging results, they still leave a performance space that can be further improved since (1) the thresholds involved are optimized independently from each other, and (2) the ordinal constraints just associate with class means (or say centroids) which are generally under-represented for class distributions. Motivated by the analysis, in this work we propose to jointly learn the thresholds across samples and class centroids by seeking an optimal direction along which all the samples are distributed as in order as possible and maximally cater for nearest-centroid distributions, which we call Ordinal Nearest-Centroid Projection (OrNCP) and is formulated as a combinatorial optimization problem. For efficiency of optimization, we further relax the problem to a quadratic programming (QP-OrNCP) that in form covers the KDLOR and MOR as its special cases. Finally, through extensive experiments on synthetic and real ordinal datasets, we demonstrate the superiority of the proposed method, over state-of-the-art methods. 
A novel ordinal learning strategy: Ordinal nearest-centroid projection