A Constrained Deep Neural Network for Ordinal Regression

Ordinal regression is a supervised learning problem aiming to classify instances into ordinal categories. It is challenging to automatically extract high-level features for representing intraclass information and interclass ordinal relationship simultaneously. This paper proposes a constrained optimization formulation for the ordinal regression problem which minimizes the negative loglikelihood for multiple categories constrained by the order relationship between instances. Mathematically, it is equivalent to an unconstrained formulation with a pairwise regularizer. An implementation based on the CNN framework is proposed to solve the problem such that high-level features can be extracted automatically, and the optimal solution can be learned through the traditional back-propagation method. The proposed pairwise constraints make the algorithm work even on small datasets, and a proposed efficient implementation make it be scalable for large datasets. Experimental results on four real-world benchmarks demonstrate that the proposed algorithm outperforms the traditional deep learning approaches and other state-of-the-art approaches based on hand-crafted features.