Mihaela Vajiac

Daniel Alpay, Kamal Diki, Mihaela Vajiac

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.

Daniel Alpay, Kamal Diki, Mihaela Vajiac

In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra.