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

arXiv: https://arxiv.org/abs/2011.00307 · HTML: https://mlsanity.com/paper/2011.00307/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Generalized Image Reconstruction over T-Algebra](https://mlsanity.com/paper/2101.06650/) (2021)
- [Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra](https://mlsanity.com/paper/2202.00450/) (2022)
- [Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra](https://mlsanity.com/paper/2308.02621/) (2023)

## Abstract (arXiv)

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.