Lattice Linear Discriminant Analysis for Shape Constrained Classification
Geng Sheng Deng, Yaoguo Xie, Xindong Wang, Qiang Fu · Frontiers in artificial intelligence and applications · 2022
Recently shape constrained classification has gained popularity in the machine learning literature in order to exploit extra model information besides raw data features. In this paper, we present a new Lattice Linear Discriminant Analysis (Lattice-LDA) classifier, which allows to take shape constraints of data inputs, such as monotonicity and convexity/concavity. Lattice-LDA constructs a nonparametric nonlinear discriminant hyperplane for classification, using an additive format of 1-D lattice functions (piecewise linear functions). Moreover, the new classifier features in taking complex shape constraints including combinations of shapes or S-shape. We optimize the model parameters using the Adaptive Moment Estimation (Adam) algorithm embedding stepwise projections which guarantee feasibility of the shape constraints. Through simulation and real-world examples, we demonstrate that the new classifier could accurately recover the nonlinear marginal effect functions and improve classification accuracy when additional shape information is present.