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We consider a novel backward-compatible paradigm of general data analyticsover a recently-reported semisimple algebra (called t-algebra). We study theabstract algebraic framework over the t-algebra by representing the elements oft-algebra by fix-sized multi-way arrays of complex numbers and the algebraicstructure over the t-algebra by a collection of direct-product constituents.Over the t-algebra, many algorithms are generalized in a straightforward mannerusing this new semisimple paradigm. To demonstrate the new paradigm'sperformance and its backward-compatibility, we generalize some canonicalalgorithms for visual pattern analysis. Experiments on public datasets showthat the generalized algorithms compare favorably with their canonicalcounterparts.

General Data Analytics with Applications to Visual Information Analysis: A Provable Backward-Compatible Semisimple Paradigm over T-Algebra