Tackle balancing constraints in semi-supervised ordinal regression

Semi-supervised ordinal regression (S²OR) has been recognized as a valuable technique to improve the performance of the ordinal regression (OR) model by leveraging available unlabeled samples. The balancing constraint is a useful approach for semi-supervised algorithms, as it can prevent the trivial solution of classifying a large number of unlabeled examples into a few classes. However, rapid training of the S²OR model with balancing constraints is still an open problem due to the difficulty in formulating and solving the corresponding optimization objective. To tackle this issue, we propose a novel form of balancing constraints and extend the traditional convex–concave procedure (CCCP) approach to solve our objective function. Additionally, we transform the convex inner loop (CIL) problem generated by the CCCP approach into a quadratic problem that resembles support vector machine, where multiple equality constraints are treated as virtual samples. As a result, we can utilize the existing fast solver to efficiently solve the CIL problem. Experimental results conducted on several benchmark and real-world datasets not only validate the effectiveness of our proposed algorithm but also demonstrate its superior performance compared to other supervised and semi-supervised algorithms