Perspective Chapter: Lattice Function-Based Support Vector Machine for Shape-Constrained Classification

Abstract

Shape-constrained classification is an important and evolving topic within machine learning, offering insights into enhancing model accuracy and interpretability through the integration of shape information from input features. In this paper, we present a novel Lattice Support Vector Machine (Lattice-SVM) classifier, which accommodates user-defined shape constraints, including monotonicity and convexity/concavity. Lattice-SVM constructs a nonparametric nonlinear discriminant hyperplane by integrating lattice functions. We optimize the model parameters using the Pegasos algorithm for SVM, which incorporates stepwise projections to ensure the feasibility of the shape constraints. Through a series of simulation studies and real-world examples, we illustrate how Lattice-SVM enhances classification performance and effectively captures nonlinear effects by leveraging the shape information of input features.