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 Concept Videos

Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Machines: Problem Solving II01:30

Machines: Problem Solving II

Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. Consider a lifting tong carrying a 100 kg load. It comprises movable sections DAF and CBG linked together with member AB.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Serum selenium levels and the risk of progression of laryngeal cancer.

PloS one·2018
Same author

Left-behind adolescents' hopes and fears for the future in rural China.

Journal of adolescence·2017
Same author

Predictors of survival for breast cancer patients with a BRCA1 mutation.

Breast cancer research and treatment·2017
Same author

BRCA Mutation Status Is Not Associated With Increased Hematologic Toxicity Among Patients Undergoing Platinum-Based Chemotherapy for Ovarian Cancer.

International journal of gynecological cancer : official journal of the International Gynecological Cancer Society·2017
Same author

Simvastatin blocks soluble SSAO/VAP-1 release in experimental models of cerebral ischemia: Possible benefits for stroke-induced inflammation control.

Biochimica et biophysica acta. Molecular basis of disease·2017
Same author

Low Arid1a Expression Correlates with Poor Prognosis and Promotes Cell Proliferation and Metastasis in Osteosarcoma.

Pathology oncology research : POR·2017
Same journal

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

IEEE transactions on neural networks·2013
Same journal

Guest editorial: special section on white box nonlinear prediction models.

IEEE transactions on neural networks·2011
Same journal

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

IEEE transactions on neural networks·2011
Same journal

Guest editorial: special section on data-based control, modeling, and optimization.

IEEE transactions on neural networks·2011
Same journal

Neural network-based multiple robot simultaneous localization and mapping.

IEEE transactions on neural networks·2011
Same journal

Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems.

IEEE transactions on neural networks·2011
See all related articles

Related Experiment Videos

Sparse approximation through boosting for learning large scale kernel machines.

Ping Sun1, Xin Yao

  • 1Centre of Excellence for Research in Computational Intelligence and Applications (CERCIA), University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. ping.sun@bhwp.nhs.uk

IEEE Transactions on Neural Networks
|April 23, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces an ensemble method for sparse approximation in large kernel machines. By adding multiple basis vectors per step, it significantly reduces computational cost and improves efficiency for large datasets.

Related Experiment Videos

Area of Science:

  • Machine Learning
  • Computational Science

Background:

  • Sparse approximation is key for large-scale kernel machines.
  • Current methods select basis vectors sequentially, leading to high computational costs.
  • Limited resources restrict the number of basis vectors, impacting solution quality.

Purpose of the Study:

  • To propose an efficient sparse approximation method for large kernel machines.
  • To address the computational and memory limitations of existing techniques.
  • To enhance the performance and scalability of kernel machine learning.

Main Methods:

  • Introduced an ensemble approach adding multiple basis vectors per forward selection step.
  • Leveraged principles similar to gradient boosting for improved efficiency.
  • Evaluated the method on large-scale regression and classification tasks.

Main Results:

  • The proposed ensemble method significantly reduces the number of required forward steps (M).
  • This reduction leads to substantial savings in computational cost and memory usage.
  • Effectiveness demonstrated across multiple large-scale regression and classification problems.

Conclusions:

  • The ensemble sparse approximation method offers a more efficient alternative for large kernel machines.
  • It effectively overcomes the limitations of sequential basis vector selection.
  • The approach shows promise for handling large datasets where computational resources are constrained.