A LAD-based evolutionary solution procedure for binary classification problems

Logical analysis of data (LAD) is a data analysis methodology used to solve the binary classification problem via supervised learning based on optimization, combinatorics, and Boolean functions. The LAD framework consists of the following four steps: data binarization, support set generation, pattern generation, and theory formulation. Patterns that contain the hidden structural information calculated from the binarized training data play the most important roles in the theory model, which consists of a union of patterns and allows for the classification of new observations. In this work, we develop a parameterized iterative genetic algorithm (PI-GA) to generate a set of patterns with good characteristics in terms of degree (simplicity-wise preference) and coverage (evidential preference) of patterns. The proposed PI-GA can generate simplicity-wise preferred patterns that also have high coverage through population structure. We show the efficiency and accuracy of the proposed pattern generation method through numerical experiments on benchmark machine learning datasets