Perceptron Ranking Using Interval Labels with Ramp Loss for Online Ordinal Regression

Due to its wide applications and learning efficiency, online ordinal regression using perceptron algorithms with interval labels (PRIL) has been increasingly applied to solve ordinal ranking problems. However, it is still a challenge for the PRIL method to handle noise labels, in which case the ranking results may change dramatically. To tackle this problem, in this paper, we propose noise-resilient online learning algorithms using ramp loss function, called PRIL-RAMP, and its nonlinear variant K-PRIL-RAMP, to improve the performance of PRIL method for noisy data streams. The proposed algorithms iteratively optimize the decision function under the framework of online gradient descent (OGD), and we justify the algorithms by showing the order preservation of thresholds. It is validated in the experiments that both approaches are more robust and efficient to noise labels than state-of-the-art online ordinal regression algorithms on real-world datasets.