Information 2012, 3(4), 756-770; doi:10.3390/info3040756

Quaternionic Multilayer Perceptron with Local Analyticity

1,* email, 2email and 1email
Received: 11 September 2012; in revised form: 13 November 2012 / Accepted: 20 November 2012 / Published: 28 November 2012
(This article belongs to the Special Issue Brain like Computing, Communication and Machines)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: A multi-layered perceptron type neural network is presented and analyzed in this paper. All neuronal parameters such as input, output, action potential and connection weight are encoded by quaternions, which are a class of hypercomplex number system. Local analytic condition is imposed on the activation function in updating neurons’ states in order to construct learning algorithm for this network. An error back-propagation algorithm is introduced for modifying the connection weights of the network.
Keywords: quaternion; local analyticity; Wirtinger calculus; multilayer perceptron; error back-propagation
PDF Full-text Download PDF Full-Text [155 KB, uploaded 28 November 2012 13:54 CET]

Export to BibTeX |

MDPI and ACS Style

Isokawa, T.; Nishimura, H.; Matsui, N. Quaternionic Multilayer Perceptron with Local Analyticity. Information 2012, 3, 756-770.

AMA Style

Isokawa T, Nishimura H, Matsui N. Quaternionic Multilayer Perceptron with Local Analyticity. Information. 2012; 3(4):756-770.

Chicago/Turabian Style

Isokawa, Teijiro; Nishimura, Haruhiko; Matsui, Nobuyuki. 2012. "Quaternionic Multilayer Perceptron with Local Analyticity." Information 3, no. 4: 756-770.

Information EISSN 2078-2489 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert