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

Abstract

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.

38 page, 12 figures. two typos are removed. Official code repository: https://github.com/liaoliang2020/talgebra