# Algebraic foundations of split hypercomplex nonlinear adaptive filtering

arXiv: https://arxiv.org/abs/1306.1676 · HTML: https://mlsanity.com/paper/1306.1676/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2013.

## Built on by (most cited first, 1 of 1)

- [Fully tensorial approach to hypercomplex-valued neural networks](https://mlsanity.com/paper/2407.00449/) (2024)

## Abstract (arXiv)

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g. for quaternions). Already in the case of quaternions we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. Keywords: Quaternionic adaptive filtering, Hypercomplex adaptive filtering, Nonlinear adaptive filtering, Hypercomplex Multilayer Perceptron, Clifford geometric algebra