Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

An Extension of the Back-Propagation Algorithm to Complex Numbers.

Tohru Nitta1

  • 1Electrotechnical Laboratory, Ibaraki, Japan

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
Summary

This study introduces Complex-BP, a complex-valued back-propagation algorithm for neural networks. It offers faster convergence and reduced learning standstill compared to real-valued methods.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Sequential Learning on sEMGs in Short- and Long-term Situations via Self-training Semi-supervised Support Vector Machine.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2022
Same author

Hyperbolic Gradient Operator and Hyperbolic Back-Propagation Learning Algorithms.

IEEE transactions on neural networks and learning systems·2017
Same author

Resolution of Singularities Introduced by Hierarchical Structure in Deep Neural Networks.

IEEE transactions on neural networks and learning systems·2016
Same author

Learning dynamics of a single polar variable complex-valued neuron.

Neural computation·2015
Same author

Performance Bounds of Quaternion Estimators.

IEEE transactions on neural networks and learning systems·2015
Same author

Local minima in hierarchical structures of complex-valued neural networks.

Neural networks : the official journal of the International Neural Network Society·2013

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Complex-valued Neural Networks

Background:

  • Traditional back-propagation algorithms operate on real numbers.
  • Limitations exist in real-valued networks for certain complex transformations.
  • Extending neural networks to complex numbers offers potential advantages.

Purpose of the Study:

  • To introduce and analyze a complex-valued back-propagation algorithm (Complex-BP).
  • To investigate the properties and performance of Complex-BP in multi-layered neural networks.
  • To explore the capabilities of Complex-BP in handling complex-valued data and transformations.

Main Methods:

  • Development of a complex-valued version of the back-propagation algorithm.
  • Application to multi-layered neural networks with complex weights, thresholds, inputs, and outputs.

Related Experiment Videos

  • Mathematical analysis of the algorithm's convergence, generalization, and transformation capabilities.

    • Main Results:

    • Complex-BP reduces the probability of 'standstill in learning'.
    • Achieves superior average convergence speed compared to real-valued back-propagation.
    • Requires approximately half the number of parameters (weights and thresholds) compared to real-valued counterparts.
    • Demonstrates ability to perform geometric transformations (rotation, similarity, displacement) that real-valued networks cannot.
    • Generalization performance remains comparable to real-valued networks.

    Conclusions:

    • Extending neural networks to complex numbers, via Complex-BP, unlocks novel capabilities.
    • Complex-BP offers significant advantages in efficiency and transformative power.
    • The algorithm provides a new avenue for advanced neural network applications handling complex data.