Supervised learning of local projection kernels

We formulate a supervised, localized dimensionality reduction method using a gating model that divides up the input space into regions and selects the dimensionality reduction projection separately in each region. The gating model, the locally linear projections, and the kernel-based supervised learning algorithm which uses them in its kernels are coupled and their training is performed with an alternating optimization procedure. Our proposed local projection kernel projects a data instance into different feature spaces by using the local projection matrices, combines them with the gating model, and performs the dot product in the combined feature space. Empirical results on benchmark data sets for visualization and classification tasks validate the idea. The method is generalizable to regression estimation and novelty detection.