Higher-order sliced inverse regressions

With the advancement of modern technology, array-valued data are often encountered in application. Such data can exhibit both high dimensionality and complex structures. Traditional methods for sufficient dimension reduction (SDR) are generally inefficient for array-valued data as they cannot adequately capture the underlying structure. In this article, we discuss recently developed higher-order approaches to SDR for regressions with matrix- or array-valued predictors, with a special focus on sliced inverse regressions. These methods can reduce an array-valued predictor's multiple dimensions simultaneously without losing much/any information for prediction and classification. We briefly discuss the implementation procedure for each method.