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Related Concept Videos

Quadratic Models01:23

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Related Experiment Video

Updated: Jul 19, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Kernel least-squares models using updates of the pseudoinverse.

E Andelić1, M Schafföner, M Katz

  • 1andelic@iesk.et.uni-magdeburg.de

Neural Computation
|October 21, 2006
PubMed
Summary

This study introduces a greedy forward selection method for sparse nonlinear models in reproducing kernel Hilbert spaces (RKHSs). This approach efficiently solves least-squares problems with computational time linear to selected training samples.

Related Experiment Videos

Last Updated: Jul 19, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Machine Learning
  • Kernel Methods
  • Computational Statistics

Background:

  • Sparse nonlinear models are crucial for complex data analysis.
  • Reproducing Kernel Hilbert Spaces (RKHSs) provide a powerful framework for nonlinear modeling.
  • Existing methods can be computationally intensive for large datasets.

Purpose of the Study:

  • To develop an efficient algorithm for sparse nonlinear classification and regression in RKHSs.
  • To address the computational challenges associated with overdetermined least-squares problems in RKHSs.
  • To enable scalable application of kernel-based nonlinear models.

Main Methods:

  • Utilized Mercer kernels and a square loss function to formulate the problem.
  • Applied a greedy forward selection scheme to iteratively build the sparse model.
  • Employed an order-recursive update of the pseudoinverse for efficient computation.

Main Results:

  • The proposed greedy forward selection method effectively solves the overdetermined least-squares problem.
  • Achieved computational time that is linear with respect to the number of selected training samples.
  • Demonstrated the feasibility of efficient sparse nonlinear modeling in RKHSs.

Conclusions:

  • The greedy forward selection algorithm offers a computationally efficient solution for sparse nonlinear modeling in RKHSs.
  • This method significantly reduces the computational burden, making RKHS models more scalable.
  • The findings pave the way for broader applications of kernel-based nonlinear methods in machine learning and statistics.