Two Bicomplex and One Multicomplex Least Mean Square algorithms

Daniel Alpay; Kamal Diki; Mihaela Vajiac

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arXiv · 2209.11899

Two Bicomplex and One Multicomplex Least Mean Square algorithms

Daniel Alpay·Kamal Diki·Mihaela Vajiac

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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.

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Daniel Alpay, Kamal Diki, Mihaela Vajiac. 2022-09-24. Two Bicomplex and One Multicomplex Least Mean Square algorithms. https://arxiv.org/abs/2209.11899

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