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Sufficient dimension reduction is a useful tool for studying the dependence between a response and a multi-dimensional predictor. In this article, a new formulation is proposed that is based on the Hellinger integral of order two, introduced as a natural measure of the regression information contained in the predictor subspace. The response may be either continuous or discrete. We establish links between local and global central subspaces, and propose an efficient local estimation algorithm. Simulations and an application show that our method compares favourably with existing approaches.