SRD: Sparse ramp discrimination for classification and variable selection on high-dimensional biological data

A massive amount of biological data generates a high volume of information. However, high-dimensional and noisy data also present significant challenges for data analysis, particularly in pattern classification. Many large-margin classification methods follow a regularization framework with the 'loss + penalty' structure. By incorporating LASSO or elastic-net penalties, we may perform classification and variable selection simultaneously. Most large margin methods rely on convex loss functions, which are computationally advantageous but provide poor approximations of the 0-1 loss due to their unbounded nature. In contrast, non-convex loss functions offer better approximations and greater robustness to outliers. We propose the sparse ramp discrimination (SRD) method, which integrates the non-convex smoothed ramp loss function with the elastic-net penalty. We apply the difference of the convex (d.c.) algorithm to efficiently solve the non-convex optimization problem through a sequence of convex subproblems. The robustness of SRD makes it well-suited for noisy, high-dimensional biological data. The performance of the proposed SRD is illustrated through simulation studies and on a colon cancer involving high throughput biological datasets.