On fused dimension reduction in multivariate regression

High-dimensional data analysis often suffers the so-called curse of dimensionality, and various data reduction methods are adopted in order to avoid it in practice. Consequently, in multivariate regression, high-dimensional predictors should be reduced to lower-dimensional ones without the loss of information, following a notion of sufficient dimension reduction. In this paper, a fused clustered seeded reduction approach is proposed for multivariate regression. The proposed method utilizes two types of information: supervised learning between the responses and the predictors, and unsupervised learning of the predictors alone. Fusing all the information has a potential advantage in the accuracy of the reduction of predictors. Numerical studies and a real data analysis confirm the practical usefulness of the proposed approach over existing methods.