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

A unified algorithm for principal and minor components extraction.

Qin Lin1, Shun Ichi Amari, Tianping Chen

  • 1Department of Mathematics, Fudan University, Shanghai, China

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
Summary
This summary is machine-generated.

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

Long-term outcomes of adjuvant metronomic capecitabine in locoregionally advanced nasopharyngeal carcinoma: a randomized, controlled, multicenter, phase 3 study.

Nature cancer·2026
Same author

Large-scale and high-resolution mass spectrometry-based proteomics defines molecular subtypes of nasopharyngeal carcinoma for therapeutic targeting.

Signal transduction and targeted therapy·2026
Same author

A bilayer theranostic hydrogel integrating visual pH monitoring with synergistic diabetic wound healing treatment.

Journal of materials chemistry. B·2026
Same author

Clinically indicated versus routine replacement of peripheral intravenous cannulas in elderly patients: Secondary analysis of a multi-center randomized controlled trial in mainland China.

Geriatric nursing (New York, N.Y.)·2026
Same author

PET-Guided Modeling of Mucosal Boron Heterogeneity Improves Dose-Toxicity Prediction in BNCT.

International journal of radiation oncology, biology, physics·2026
Same author

Application of SPI-guided analgesia in laparoscopic gynecologic surgery: a randomized controlled trial evaluating the remifentanil-sparing effect and predictive value of time-weighted SPI.

Journal of clinical monitoring and computing·2026
Same journal

Dynamic analysis and reliable mechanical optimization application of ring HNN effected with a memristive neuron.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

DAFF-Net: A detection and search method for small-scale low surface brightness galaxies.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Quasi-synchronization for complex networks with hybrid pinning intermittent control.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Physics-encoded convolutional neural operators for parametric PDEs: A convergence-guaranteed framework via pre-computed kernel fields.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Exploiting audio-visual modalities in videos: Object detection via multi-stage bilateral coupling network.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Reliability-aware modality completion with cross-modal distillation for federated learning with missing modalities.

Neural networks : the official journal of the International Neural Network Society·2026
See all related articles

A new unified algorithm simplifies minor component extraction, previously challenging compared to principal component extraction. This method is significant for neural network implementation and uses natural gradient ascent/descent methods.

Area of Science:

  • Information Processing
  • Machine Learning
  • Linear Algebra

Background:

  • Principal Component Analysis (PCA) and minor component analysis are crucial for data processing.
  • Conventional algorithms face significant challenges in minor component extraction compared to principal component extraction.

Purpose of the Study:

  • To propose a unified algorithm for extracting both principal and minor component eigenvectors.
  • To demonstrate the practical significance of this unified algorithm in neural network implementation.

Main Methods:

  • Development of a unified algorithm for eigenvector extraction.
  • Utilizing natural gradient ascent/descent methods, framed as potential flow in Riemannian space.
  • Relating the proposed algorithms to existing methods like Oja's principal subspace algorithm and Brockett flow.

Related Experiment Videos

Main Results:

  • The unified algorithm successfully extracts true principal components.
  • A simple sign alteration enables the same algorithm to extract true minor components.
  • The algorithm's foundation in natural gradient methods is established.

Conclusions:

  • The proposed unified algorithm offers a more efficient approach to both principal and minor component extraction.
  • This method has direct practical applications in the field of neural networks.
  • The algorithm provides a novel perspective on eigenvector extraction through Riemannian geometry and natural gradients.