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Relaxation of Skeletal Muscles01:29

Relaxation of Skeletal Muscles

The period of muscle contraction primarily influences the duration of stimulation at the neuromuscular junction (NMJ), the presence of free calcium ions in the sarcoplasm, and the availability of energy or ATP to support contractions.
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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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Regression Toward the Mean01:52

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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...

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Related Experiment Video

Updated: Jul 7, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

Successive overrelaxation for support vector machines.

O L Mangasarian1, D R Musicant

  • 1Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA.

IEEE Transactions on Neural Networks
|February 7, 2008
PubMed
Summary
This summary is machine-generated.

Successive overrelaxation (SOR) effectively trains support vector machines (SVMs) for massive datasets. This method processes large-scale data efficiently, outperforming other algorithms on big discrimination tasks.

Related Experiment Videos

Last Updated: Jul 7, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

Area of Science:

  • Machine Learning
  • Optimization Algorithms

Background:

  • Training support vector machines (SVMs) on massive datasets presents significant computational challenges.
  • Conventional linear and quadratic programming methods struggle with datasets containing millions of points.

Purpose of the Study:

  • To introduce and evaluate the Successive Overrelaxation (SOR) algorithm for training SVMs on extremely large datasets.
  • To demonstrate SOR's capability in handling data that exceeds available memory.

Main Methods:

  • Utilized Successive Overrelaxation (SOR) for symmetric linear complementarity problems and quadratic programs to train SVMs.
  • Compared SOR's performance against Platt's Sequential Minimal Optimization (SMO) and Joachims' SVMlight algorithms.
  • Applied SOR to datasets with up to 10,000,000 points.

Main Results:

  • SOR successfully trained SVMs on massive datasets, processing one point at a time, thus not requiring data to reside in memory.
  • The algorithm demonstrated linear convergence to a solution.
  • Numerical results showed SOR's effectiveness on datasets up to 10 million points, solving problems intractable for other methods.
  • On smaller datasets, SOR was faster than SVMlight and comparable or faster than SMO.

Conclusions:

  • Successive Overrelaxation (SOR) offers a viable and efficient solution for training support vector machines on massive datasets.
  • SOR's ability to handle large-scale data makes it a significant advancement for discrimination problems previously unsolvable by conventional techniques.