Neural networks and principal component analysis: Learning from examples without local minima
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Learning Internal Representations by Error Propagation
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1985) · doi:10.21236/ada164453 · Cited by 16,501 · see citing works
An introduction to computing with neural nets
Lippmann, R. P. (1987) · IEEE ASSP Magazine · doi:10.1109/massp.1987.1165576 · Cited by 7,848 · see citing works
Introduction to Numerical Analysis.
Fröberg, C.-E., Stoer, J., & Bulirsch, R. Z. (1981) · Mathematics of Computation · doi:10.2307/2007454 · Cited by 5,510 · see citing works
A learning algorithm for Boltzmann machines
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985) · Cognitive Science · doi:10.1207/s15516709cog0901_7 · Cited by 3,402 · see citing works
An Introduction to Numerical Analysis
S., F., & ATKINSON, K. E. (1990) · Mathematics of Computation · doi:10.2307/2008519 · Cited by 3,093 · see citing works
Simplified neuron model as a principal component analyzer
Oja, E. (1982) · Journal of Mathematical Biology · doi:10.1007/bf00275687 · Cited by 2,309 · see citing works
Nonlinear neural networks: Principles, mechanisms, and architectures
Grossberg, S. (1988) · Neural Networks · doi:10.1016/0893-6080(88)90021-4 · Cited by 1,623 · see citing works
Auto-association by multilayer perceptrons and singular value decomposition
Bourlard, H., & Kamp, Y. (1988) · Biological Cybernetics · doi:10.1007/bf00332918 · Cited by 1,332 · see citing works
An introduction to computing with neural nets
Lippmann, R. P. (1988) · ACM SIGARCH Computer Architecture News · doi:10.1145/44571.44572 · Cited by 540 · see citing works
Introduction to Numerical Analysis
Spencer, A. J. M., Parker, D. F., Berry, D. S., et al. (1977) · Engineering Mathematics · doi:10.1007/978-94-010-9311-8_9 · Cited by 467 · see citing works
From basic network principles to neural architecture: emergence of spatial-opponent cells.
Linsker, R. (1986) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.83.19.7508 · Cited by 386 · see citing works
Learning the hidden structure of speech
Elman, J. L., & Zipser, D. (1988) · The Journal of the Acoustical Society of America · doi:10.1121/1.395916 · Cited by 272 · see citing works
From basic network principles to neural architecture: emergence of orientation-selective cells.
Linsker, R. (1986) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.83.21.8390 · Cited by 244 · see citing works
Symmetry, 0-1 Matrices and Jacobians: A Review
Magnus, J. R., & Neudecker, H. (1986) · Econometric Theory · doi:10.1017/s0266466600011476 · Cited by 113 · see citing works
Clark-Carter, D. D. (2023) · Routledge eBooks · doi:10.4324/9781003208419-29 · Cited by 111 · see citing works
Harvey, A. C., & Pollock, D. S. G. (1981) · Economica · doi:10.2307/2552951 · Cited by 56 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570 · see citing works
Neural Networks and the Bias/Variance Dilemma
Geman, S., Bienenstock, E., & Doursat, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.1.1 · Cited by 3,578 · see citing works
Nonlinear principal component analysis using autoassociative neural networks
Kramer, M. A. (1991) · AIChE Journal · doi:10.1002/aic.690370209 · Cited by 3,037 · see citing works
Machine Learning for Fluid Mechanics
Brunton, S. L., Noack, B. R., & Koumoutsakos, P. (2020) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010719-060214 · Cited by 3,063 · see citing works
Lin, T., & Zha, H. (2008) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2007.70735 · Cited by 446 · see citing works
The dropout learning algorithm
Baldi, P., & Sadowski, P. (2014) · Artificial Intelligence · doi:10.1016/j.artint.2014.02.004 · Cited by 340 · see citing works
Self-citationDeep learning for human affect recognition: Insights and new developments
Rouast, P. V., Adam, M. T. P., & Chiong, R. (2021) · IEEE Transactions on Affective Computing · doi:10.1109/taffc.2018.2890471 · Cited by 243 · see citing works
Computational Capabilities of Graph Neural Networks
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., & Monfardini, G. (2009) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2008.2005141 · Cited by 225 · see citing works
Factor Models, Machine Learning, and Asset Pricing
Giglio, S., Kelly, B., & Xiu, D. (2022) · Annual Review of Financial Economics · doi:10.1146/annurev-financial-101521-104735 · Cited by 187 · see citing works
Optimizing Autoencoders for Learning Deep Representations from Health Data
Zhou, C., Jia, Y., & Motani, M. (2019) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2018.2856820 · Cited by 29 · see citing works
How Adversarial REM Dreams May Facilitate Creativity, and Why We Become Aware of Them
Deperrois, N., Petrovici, M., Jordan, J., Huber, L., & Senn, W. (2024) · Clinical and Translational Neuroscience · doi:10.3390/ctn8020021 · Cited by 3 · see citing works
“The visualization is not part of the model, although PCA could itself be modeled by a neuronal network [29].”
Method
- Authors
- Baldi, P., & Hornik, K.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Baldi, Pierre
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 1989-01
- Volume
- 2
- Issue
- 1
- Pages
- 53-58
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2078626246
- Cited by
- 1,383
- References
- 16
- Citations by year
- 2026: 39 · 2025: 51 · 2024: 52 · 2023: 61 · 2022: 82 · 2021: 126 · 2020: 106 · 2019: 86 · 2018: 87 · 2017: 62 · 2016: 49 · 2015: 27 · 2014: 28 · 2013: 19 · 2012: 19
- FWCI
- 19.82
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Networks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
- Keywords
- feedforward neural networks, principal component analysis, saddle points, local minima, backpropagation, covariance matrix, training patterns, critical points
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review