In this paper, a combined nonlinear dimensionality reduction and multiclass classification framework is proposed. Specifically, a novel discriminant analysis (DA) technique, called accelerated kernel subclass discriminant analysis (AKSDA), derives a discriminant subspace, and a linear multiclass support vector machine (MSVM) computes a set of separating hyperplanes in the derived subspace. Moreover, within this framework an approach for accelerating the computation of multiple Gram matrices and an associated late fusion scheme are presented. Experimental evaluation in five multimedia datasets, on tasks such as video event detection and news document classification, shows that the proposed framework achieves excellent results in terms of both training time and generalization performance.