Dimensionality reduction (DR) is critical to many machine learning and signal processing tasks involving high-dimensional large-scale data. Standard DR tools such as principal component analysis (PCA) deal with a single dataset at a time. In diverse practical settings however, one is often tasked with learning the discriminant subspace such that one dataset of particular interest (a.k.a., target data) lies on, whereas the other dataset(s) (a.k.a., control data) do not. This is what is known as discriminative DR. Building on but considerably generalizing existing linear variants, this contribution puts forth a novel nonlinear approach for discriminative DR of multiple datasets through kernel-based learning. Interestingly, its solution can be provided analytically in terms of a generalized eigenvalue decomposition problem, for which various efficient solvers are available. Numerical experiments using synthetic and real data showcase the merits of the proposed nonlinear discriminative DR approach relative to state-of-the-art alternatives.