Lattice Linear Discriminant Analysis for Shape Constrained Classification

Recently shape constrained classification has gained popularity in the machine learning literature 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 take constraints of inputs, such as monotonicity and convexity/concavity. Lattice-LDA constructs nonparametric nonlinear discriminant hyperplane for classification, using an additive format 1-D lattice functions (piecewise linear functions). Moreover, classifier features taking complex including combinations shapes or S-shape. We optimize parameters Adaptive Moment Estimation (Adam) algorithm embedding stepwise projections guarantee feasibility constraints. Through simulation real-world examples, demonstrate that could accurately recover marginal effect improve accuracy when additional is present.