Quaternion-valued recurrent projection neural networks (QRPNNs) are obtained by combining the non-local projection learning with the quaternion-valued recurrent correlation neural network (QRCNNs). QRPNNs overcome the cross-talk problem of QRCNNs and are appropriate to implement associative memories. Furthermore, computational experiments reveal that QRPNNs exhibit greater storage capacity and noise tolerance than their corresponding QRCNNs.

This repository contain the Julia source-codes of QRPNNs on unit quaternions, as described in the paper "Quaternion-Valued Recurrent Projection NeuralNetworks on Unit Quaternions" by Marcos Eduardo Valle and Rodolfo Lobo (see https://arxiv.org/abs/2001.11846). The Jupyter-notebook of the computational experimens are also available in this repository.

First of all, call the QRPNN module using:

include("QRPNN.jl")

Define a real-valued excitation function f. Examples of excitation functions are provided in the QRPNN.jl including:

QRPNN.identity, QRPNN.exponential, QRPNN.potential, and QRPNN.high_order

Given a quaternion-valued matrix U=[u1,...,up] of size NxP whose columns correspond to the fundamental memories, train the QRPNN using the command:

V = QRPNN.train(f,f_params,U)

where f_params are the parameters of f.

Given an input quaternion-valued vector x of length N, the output is given by

y = QRPNN.main(f,f_parameters, U, V, x, it_max, verbose)

where it_max (default is it_max = 1000) is the maximum number of iterations and verbose (default is true) informs if the maximum number of iterations has been reached.

For example, the exponential quaternion-valued recurrent projection neural network with parameter alpha = 10 adn the default maximum number of iteration is called using the command:

y = QRPNN.main(QRPNN.exponential, 10, U, V, x)

Remark: Quaternion-valued Recurrent Correlation Neural Network (see https://doi.org/10.1109/IJCNN.2018.8489714) is obtained by considering V = U (without training).

• Marcos Eduardo Valle and Rodoldo Lobo - University of Campinas