Maximum Gradient Dimensionality Reduction

We propose a novel dimensionality reduction approach based on the gradient of the regression function. Our approach is conceptually similar to Principal Component Analysis, however instead of seeking a low dimensional representation of the predictors that preserve the sample variance, we project onto a basis that preserves those predictors which induce the greatest change in the response. Our approach has the benefits of being simple and easy to implement and interpret, while still remaining very competitive with sophisticated state-of-the-art approaches.