Approximation of Ensemble Boundary Using Spectral Coefficients

Abstract

A spectral analysis of a Boolean function is proposed for approximating the decision boundary of an ensemble of classifiers, and an intuitive explanation of computing Walsh coefficients for the functional approximation is provided. It is shown that the difference between the first- and third-order coefficient approximations is a good indicator of optimal base classifier complexity. When combining neural networks, the experimental results on a variety of artificial and real two-class problems demonstrate under what circumstances ensemble performance can be improved. For tuned base classifiers, the first-order coefficients provide performance similar to the majority vote. However, for weak/fast base classifiers, higher order coefficient approximation may give better performance. It is also shown that higher order coefficient approximation is superior to the Adaboost logarithmic weighting rule when boosting weak decision tree base classifiers.