Deep Orientational Representation Learning for Ordinal Regression

Ordinal regression aims to predict ordered classes. Existing methods mainly focus on label distribution shapes and feature distance relationships, while the directional characteristics in the representation space remain underexplored. In this paper, we propose deep orientational representation learning (ORL), aiming to ensure the trajectory of features sequentially connected by ordinal categories approximates a geodesic. We treat the output layer weights as ordinal prototypes and introduce two constraints, the co-directional constraint and the counter-directional constraint. They operate by constraining the angles between pairs of vectors. The former minimizes the angle between vectors with matching start and end categories, while the latter maximizes the angle between vectors whose start categories are the same but whose end categories are on opposite sides. The two constraints optimize the representation from different ordinal directions. ORL is extended to a multi-prototype setting (MORL) to mitigate misalignment between features and oriented prototypes caused by large intra-class variations. Theoretical analysis links ORL to distribution unimodality and distance orderliness, highlighting its advantages. The effectiveness of ORL (MORL) is demonstrated on various tasks including facial age estimation, historical image dating, and aesthetic quality assessment.