Abstract: Existing regression dimension-reduction methods estimate a subspace in the primal predictor-based space, and then obtain the set of reduced predictors by projecting the original predictor vector onto this subspace. We propose a principled method for estimating a sufficient reduction in the dual sample-based space, based on a supervised inverse regression model. The reduction is performed without needing to estimate the subspace. Our method extends the duality between principal component analysis and principal coordinate analysis. We study the asymptotic behavior of the proposed method, and demonstrate that it is robust to model misspecification. We present simulation results to support the theoretical conclusion, and show how to apply the method by means of a real-data analysis.

Key words and phrases: Data visualization, inverse model-based reduction, multi- dimensional scaling, sufficient dimension reduction, supervised coordinate analysis.