Metric Learning for Ordinal Data

A large amount of ordinal-valued data exist in many domains, including medical and health science, social science, economics, political science, etc. Unlike image and speech datasets of real-valued data, learning with ordinal variables (i.e., features) presents unique challenges. In particular, the nominal differences between those feature values, which are just ranks, do not necessarily correspond to the real distances between the corresponding categories. Given their wide existence, it is imperative to develop machine learning algorithms that specifically address the need to model and infer with such data. In this paper, we present a novel metric learning algorithm that takes into consideration the nature of ordinal data. Our approach treats ordinal values as latent variables in intervals. Our algorithm then learns what those intervals are as well as distance metrics to measure distances between latent variables in those intervals. We derive the corresponding optimization algorithm and demonstrate how that can be solved effectively. Experimental results show that the proposed approach significantly improves baselines that do not explicitly model ordinal features.