A Forward Approach for Sufficient Dimension Reduction in Binary Classification for Large-scale Data

Sufficient dimension reduction, aimed at finding a lower-dimensional subspace in explanatory variables that contains response variable information, typically relies on inverse-based methodologies. These methods are easy to implement but often require linear or constant variance conditions. To address these limitations, techniques for forwardly estimating the central subspace have been developed. In particular, methods utilizing the Reproducing Kernel Hilbert Space have gained attention, but their use in analyzing large datasets is limited due to the characteristics of the kernel space. In this paper, we study a novel forward approach for sufficient dimension reduction in binomial classification of large-scale data. We propose a method that employs a divide-and-conquer technique to split data into subsets, then independently perform dimension reduction on each subset before synthesizing them into a final model. It was shown that when the number of partitions of data was appropriately selected, the loss in prediction accuracy was not significant compared to the existing method, while being efficient in terms of storage space and calculation cost. In addition, simulations in various models showed superior prediction accuracy than other inverse-based techniques. The utility of the proposed method was confirmed through the real data analysis.