  The purpose of sufficient dimension reduction (SDR) is to find the
low-dimensional subspace of input features that is sufficient for predicting
output values. In this paper, we propose a novel distribution-free SDR method
called sufficient component analysis (SCA), which is computationally more
efficient than existing methods. In our method, a solution is computed by
iteratively performing dependence estimation and maximization: Dependence
estimation is analytically carried out by recently-proposed least-squares
mutual information (LSMI), and dependence maximization is also analytically
carried out by utilizing the Epanechnikov kernel. Through large-scale
experiments on real-world image classification and audio tagging problems, the
proposed method is shown to compare favorably with existing dimension reduction
approaches.
