General Data Analytics with Applications to Visual Information Analysis: A Provable Backward-Compatible Semisimple Paradigm over T-Algebra
This work addresses the need for flexible and compatible data analysis methods, particularly in visual information analysis, but it appears incremental as it builds on existing algorithms.
The paper tackles the problem of generalizing data analytics algorithms by introducing a backward-compatible semisimple paradigm over t-algebra, and experiments on public datasets show that the generalized algorithms perform favorably compared to canonical counterparts.
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.