Sparse ordinal discriminant analysis

Ordinal class labels are frequently observed in classification studies across various fields. In medical science, patients' responses to a drug can be arranged in the natural order, reflecting their recovery postdrug administration. The severity of the disease is often recorded using an ordinal scale, such as cancer grades or tumor stages. We propose a method based on the linear discriminant analysis (LDA) that generates a sparse, low-dimensional discriminant subspace reflecting the class orders. Unlike existing approaches that focus on predictors marginally associated with ordinal labels, our proposed method selects variables that collectively contribute to the ordinal labels. We employ the optimal scoring approach for LDA as a regularization framework, applying an ordinality penalty to the optimal scores and a sparsity penalty to the coefficients for the predictors. We demonstrate the effectiveness of our approach using a glioma dataset, where we predict cancer grades based on gene expression. A simulation study with various settings validates the competitiveness of our classification performance and demonstrates the advantages of our approach in terms of the interpretability of the estimated classifier with respect to the ordinal class labels.