Maximum patterns in datasets

Given a binary dataset of positive and negative observations, a positive (negative) pattern is a subcube having a nonempty intersection with the positive (negative) subset of the dataset, and an empty intersection with the negative (positive) subset of the dataset. Patterns are the key building blocks in Logical Analysis of Data (LAD), and are an essential tool in identifying the positive or negative nature of “new” observations covered by them. We develop exact and heuristic algorithms for constructing a pattern of maximum coverage which includes a given point. It is shown that the heuristically constructed patterns can achieve more than 98% of the maximum possible coverage, while requiring only a fraction of the computing time of the exact algorithm. Maximum patterns are shown to be useful for constructing highly accurate LAD classification models. In comparisons with the commonly used machine learning algorithms implemented in the publicly available Weka software package, the implementation of LAD using maximum patterns is shown to be a highly competitive classification method. Acknowledgements: T. Bonates gratefully acknowledges the partial support of a DIMACS Graduate Student Award. We acknowledge the assistance provided by Dash Optimization by allowing the use of its integer and linear programming solver Xpress-MP within its Academic Partnership Program.