  Ordinal regression is a specialized supervised problem where the labels show
an inherent order. The order distinguishes it from normal multi-class problem.
Support Vector Ordinal Regression, as an outstanding ordinal regression model,
is widely used in many ordinal regression tasks. However, like most supervised
learning algorithms, the design of SVOR is based on the assumption that the
training data are real and reliable, which is difficult to satisfy in
real-world data. In many practical applications, outliers are frequently
present in the training set, potentially leading to misguide the learning
process, such that the performance is non-optimal. In this paper, we propose a
novel capped $\ell_{p}$-norm loss function that is theoretically robust to both
light and heavy outliers. The capped $\ell_{p}$-norm loss can help the model
detect and eliminate outliers during training process. Adhering to this
concept, we introduce a new model, Capped $\ell_{p}$-Norm Support Vector
Ordinal Regression(CSVOR), that is robust to outliers. CSVOR uses a weight
matrix to detect and eliminate outliers during the training process to improve
the robustness to outliers. Moreover, a Re-Weighted algorithm algorithm which
is illustrated convergence by our theoretical results is proposed to
effectively minimize the corresponding problem. Extensive experimental results
demonstrate that our model outperforms state-of-the-art(SOTA) methods,
particularly in the presence of outliers.
