Two Bicomplex and One Multicomplex Least Mean Square algorithms
Machine Learning
2023-12-25 v2 Information Theory
math.IT
Optimization and Control
Abstract
We study and introduce new gradient operators in the complex and bicomplex settings, inspired from the well-known Least Mean Square (LMS) algorithm invented in 1960 by Widrow and Hoff for Adaptive Linear Neuron (ADALINE). These gradient operators will be used to formulate new learning rules for the Bicomplex Least Mean Square (BLMS) algorithms and we will also formulate these learning rules will for the case of multicomplex LMS algorithms (MLMS). This approach extends both the classical real and complex LMS algorithms.
Cite
@article{arxiv.2209.11899,
title = {Two Bicomplex and One Multicomplex Least Mean Square algorithms},
author = {Daniel Alpay and Kamal Diki and Mihaela Vajiac},
journal= {arXiv preprint arXiv:2209.11899},
year = {2023}
}