  We consider a novel backward-compatible paradigm of general data analytics
over a recently-reported semisimple algebra (called t-algebra). We study the
abstract algebraic framework over the t-algebra by representing the elements of
t-algebra by fix-sized multi-way arrays of complex numbers and the algebraic
structure over the t-algebra by a collection of direct-product constituents.
Over the t-algebra, many algorithms are generalized in a straightforward manner
using this new semisimple paradigm. To demonstrate the new paradigm's
performance and its backward-compatibility, we generalize some canonical
algorithms for visual pattern analysis. Experiments on public datasets show
that the generalized algorithms compare favorably with their canonical
counterparts.
