# Convergence analysis for principal component flows

Shintaro Yoshizawa; Uwe Helmke; Konstantin Starkov

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 1, page 223-236
- ISSN: 1641-876X

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topYoshizawa, Shintaro, Helmke, Uwe, and Starkov, Konstantin. "Convergence analysis for principal component flows." International Journal of Applied Mathematics and Computer Science 11.1 (2001): 223-236. <http://eudml.org/doc/207501>.

@article{Yoshizawa2001,

abstract = {A common framework for analyzing the global convergence of several flows for principal component analysis is developed. It is shown that flows proposed by Brockett, Oja, Xu and others are all gradient flows and the global convergence of these flows to single equilibrium points is established. The signature of the Hessian at each critical point is determined.},

author = {Yoshizawa, Shintaro, Helmke, Uwe, Starkov, Konstantin},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Hessians; neural networks; principal component analysis; phase portrait; gradient flows},

language = {eng},

number = {1},

pages = {223-236},

title = {Convergence analysis for principal component flows},

url = {http://eudml.org/doc/207501},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Yoshizawa, Shintaro

AU - Helmke, Uwe

AU - Starkov, Konstantin

TI - Convergence analysis for principal component flows

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 1

SP - 223

EP - 236

AB - A common framework for analyzing the global convergence of several flows for principal component analysis is developed. It is shown that flows proposed by Brockett, Oja, Xu and others are all gradient flows and the global convergence of these flows to single equilibrium points is established. The signature of the Hessian at each critical point is determined.

LA - eng

KW - Hessians; neural networks; principal component analysis; phase portrait; gradient flows

UR - http://eudml.org/doc/207501

ER -

## References

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