  In this paper, using a novel matrix factorization and simultaneous reduction
to diagonal form approach (or in short simultaneous reduction approach),
Accelerated Kernel Discriminant Analysis (AKDA) and Accelerated Kernel Subclass
Discriminant Analysis (AKSDA) are proposed. Specifically, instead of performing
the simultaneous reduction of the between- and within-class or subclass scatter
matrices, the nonzero eigenpairs (NZEP) of the so-called core matrix, which is
of relatively small dimensionality, and the Cholesky factorization of the
kernel matrix are computed, achieving more than one order of magnitude speed up
over kernel discriminant analysis (KDA). Moreover, consisting of a few
elementary matrix operations and very stable numerical algorithms, AKDA and
AKSDA offer improved classification accuracy. The experimental evaluation on
various datasets confirms that the proposed approaches provide state-of-the-art
performance in terms of both training time and classification accuracy.
