The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Wirtinger Calculus Based Gradient Descent and Levenberg-Marquardt Learning Algorithms in Complex-Valued Neural Networks
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In the citing paper
“A solution to this problem is Wirtinger calculus [62].”
From An Introduction to Deep Learning for the Physical Layer (2017) · cites this paper as [62]
Citations
Cites
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
Training feedforward networks with the Marquardt algorithm
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Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory
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The Complex Gradient Operator and the CR-CalculusPreprint
Kreutz-Delgado, K. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0906.4835 · Cited by 560
Complex-Valued Neural Networks
Hirose, A. (2012) · Studies in Computational Intelligence · doi:10.1007/978-3-642-27632-3 · Cited by 531
Zur formalen Theorie der Funktionen von mehr komplexen Ver�nderlichen
Wirtinger, W. (1927) · Mathematische Annalen · doi:10.1007/bf01447872 · Cited by 409
A complex gradient operator and its application in adaptive array theory
Brandwood, D. H. (1983) · IEE Proceedings H Microwaves, Optics and Antennas · doi:10.1049/ip-h-1.1983.0004 · Cited by 347
Research works printed but not linked: 1
- Helstrom, C.W.: Elements of Signal Detection and Estimation. Prentice Hall, New Jersey (1995)
Cited by
An Introduction to Deep Learning for the Physical Layer
O'Shea, T., & Hoydis, J. (2017) · IEEE Transactions on Cognitive Communications and Networking · doi:10.1109/tccn.2017.2758370 · Cited by 2,980
Complex-Valued Neural Networks: A Comprehensive Survey
Lee, C., Hasegawa, H., & Gao, S. (2022) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2022.105743 · Cited by 289
Machine learning algorithms in microbial classification: a comparative analysis
Wu, Y., & Gadsden, S. A. (2023) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2023.1200994 · Cited by 56
Is a Complex-Valued Stepsize Advantageous in Complex-Valued Gradient Learning Algorithms?
Zhang, H., & Mandic, D. P. (2015) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2494361 · Cited by 53
Barrachina, J. A., Ren, C., Morisseau, C., Vieillard, G., & Ovarlez, J. (2021) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp39728.2021.9413814 · Cited by 53
Metadata
- Authors
- Amin, M. F., Amin, M. I., Al-Nuaimi, A. Y. H., & Murase, K.
- Affiliations
- University of Fukui (JP)
- Corresponding author
- Amin, Md. Faijul
- Amin, Muhammad Ilias
- Murase, Kazuyuki
- ORCID
- Murase, Kazuyuki
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2011
- Volume
- 7062
- Pages
- 550-559
- ISSN
- 0302-9743 (ISSN-L)
- 1611-3349
- OpenAlex
- W2105737828
- Cited by
- 65
- References
- 24
- Citations by year
- 2026: 5 · 2025: 4 · 2024: 8 · 2023: 8 · 2022: 6 · 2021: 1 · 2020: 1 · 2019: 5 · 2018: 6 · 2017: 6 · 2016: 4 · 2015: 4 · 2014: 2 · 2013: 1 · 2012: 4
- FWCI
- 1.85
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Lecture notes in computer science (publishedVersion)
- Lecture notes in computer science
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- complex-valued neural networks, Wirtinger calculus, gradient descent, Levenberg-Marquardt algorithm, parameter optimization, feedforward neural networks
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- This page
- CoChat. (2026). Citation check: Wirtinger Calculus Based Gradient Descent and Levenberg-Marquardt Learning Algorithms in Complex-Valued Neural Networks. https://app.cochat.ai/papers/10.1007/978-3-642-24955-6_66
- The paper
- Amin, M. F., Amin, M. I., Al-Nuaimi, A. Y. H., & Murase, K. (2011). Wirtinger Calculus Based Gradient Descent and Levenberg-Marquardt Learning Algorithms in Complex-Valued Neural Networks. Lecture Notes in Computer Science. https://doi.org/10.1007/978-3-642-24955-6_66
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
