Learning Algorithms in Quaternion Neural Networks Using GHR Calculus

Title:

Learning Algorithms in Quaternion Neural Networks Using GHR Calculus

Creator:

Xu, D., Zhang, L., and Zhang, H.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5f203a9b-096d-4109-8ab5-194ba5cfbade
uuid:5f203a9b-096d-4109-8ab5-194ba5cfbade
doi:10.14311/NNW.2017.27.014

Subject:

quaternion neural netwirks, non-analytic quaternion activation functions, GHR calculus, learning algorithms, and convergence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

One difficulty for quaternion neural networks (QNNs) is that quaternion nonlinear activation functions are usually non-analytic and thus quaternion derivatives cannot be used. In this paper, we derive the quaternion gradient descent, approximated quaternion Gauss-Newton and quaternion Levenberg-Marquardt algorithms for feedforward QNNs based on the GHR calculus, which is suitable for analytic and non-analytic quaternion functions. Meanwhile, we solve a widely linear quaternion least squares problem in the derivation of quaternion Gauss-Newton algorithm, which is more general than the usual least squares probŹlem. A rigorous analysis of the convergence of the proposed algorithms is provided. Simulations on the prediction of benchmark signals support the approach.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Source:

Neural network world: international journal on neural and mass-parallel computing and information systems | 2017 Volume:27 | Number:3

Harvested from:

CDK

Metadata only:

false