<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Hebbian learning rule is well known as a memory storing scheme for associative memory models. This scheme is simple and fast, however, its performance gets decreased when memory patterns are not orthogonal each other. Pseudo-orthogonalization is a decorrelating method for memory patterns which uses XNOR masking between the memory patterns and randomly generated patterns. By a combination of this method and Hebbian learning rule, storage capacity of associative memory concerning non-orthogonal patterns is improved without high computational cost. The memory patterns can also be retrieved based on a simulated annealing method by using an external stimulus pattern. By utilizing complex numbers and quaternions, we can extend the pseudo-orthogonalization for complex-valued and quaternionic Hopfield neural networks. In this paper, the extended pseudo-orthogonalization methods for associative memories based on complex numbers and quaternions are examined from the viewpoint of correlations in memory patterns. We show that the method has stable recall performance on highly correlated memory patterns compared to the conventional real-valued method.</p></abstract>

Hebbian learning rule is well known as a memory storing scheme for associative memory models. This scheme is simple and fast, however, its performance gets decreased when memory patterns are not orthogonal each other. Pseudo-orthogonalization is a decorrelating method for memory patterns which uses XNOR masking between the memory patterns and randomly generated patterns. By a combination of this method and Hebbian learning rule, storage capacity of associative memory concerning non-orthogonal patterns is improved without high computational cost. The memory patterns can also be retrieved based on a simulated annealing method by using an external stimulus pattern. By utilizing complex numbers and quaternions, we can extend the pseudo-orthogonalization for complex-valued and quaternionic Hopfield neural networks. In this paper, the extended pseudo-orthogonalization methods for associative memories based on complex numbers and quaternions are examined from the viewpoint of correlations in memory patterns. We show that the method has stable recall performance on highly correlated memory patterns compared to the conventional real-valued method.

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

, Japan 7-1-28 Minatojima-Minami-cho, Chuo-ku, Kobe, Hyogo, 650-0047,

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Hebbian learning rule is well known as a memory storing scheme for associative memory models. This scheme is simple and fast, however, its performance gets...

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

Published Online: May 03, 2017

Page range: 257 - 264

Received: Nov 10, 2016

Accepted: Dec 13, 2016

DOI: https://doi.org/10.1515/jaiscr-2017-0018

Keywords
Hopfield neural network, pseudo-orthogonalization, complex numbers, quaternions

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Pseudo-Orthogonalization of Memory Patterns for Complex-Valued and Quaternionic Associative Memories

Published Online: May 03, 2017

Page range: 257 - 264

Received: Nov 10, 2016

Accepted: Dec 13, 2016

DOI: https://doi.org/10.1515/jaiscr-2017-0018

KeywordsHopfield neural network, pseudo-orthogonalization, complex numbers, quaternions

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hopfield neural network, pseudo-orthogonalization, complex numbers, quaternions