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Related Concept Videos

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
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Types of Errors: Detection and Minimization01:12

Types of Errors: Detection and Minimization

Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...
Regression Toward the Mean01:52

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...
Truncation in Survival Analysis01:09

Truncation in Survival Analysis

Truncation in survival analysis refers to the exclusion of individuals or events from the dataset based on specific criteria related to the time of the event. This exclusion can happen in two primary forms: left truncation and right truncation.
Left truncation occurs when individuals who experienced the event of interest before a certain time are not included in the study. This is often due to a "delayed entry" into the study where only those who survive until a certain entry point are observed.

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Related Experiment Video

Updated: Jul 7, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Pruning error minimization in least squares support vector machines.

B J de Kruif1, T A de Vries

  • 1Drebbel Inst. for Mechatronics, Univ. of Twente, Enschede, Netherlands.

IEEE Transactions on Neural Networks
|February 2, 2008
PubMed
Summary

A new pruning method for least squares support vector machines (LSSVM) improves function approximation accuracy. This approach reliably identifies training samples that minimize approximation errors upon omission, outperforming standard pruning techniques.

Related Experiment Videos

Last Updated: Jul 7, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Area of Science:

  • Machine Learning
  • Computational Statistics

Background:

  • Support Vector Machines (SVM) are used for classification and function approximation, often employing an epsilon-insensitive cost function.
  • Least Squares Support Vector Machines (LSSVM) utilize a quadratic cost function, typically yielding non-sparse solutions in function approximation tasks.

Purpose of the Study:

  • To introduce a novel pruning procedure for LSSVM that enhances the sparseness of the model.
  • To address the limitations of standard pruning methods in accurately predicting approximation errors after data omission.

Main Methods:

  • The study proposes a new pruning scheme for LSSVM that selects training samples based on their predicted impact on approximation error.
  • This method recursively solves the approximation problem and omits data, focusing on samples that minimize error upon removal.

Main Results:

  • The introduced pruning procedure demonstrates superior performance compared to the standard pruning method for LSSVM.
  • The new scheme reliably identifies training samples whose omission results in minimal approximation error.

Conclusions:

  • The proposed pruning strategy effectively enhances model sparseness in LSSVM function approximation.
  • This method offers a more reliable approach to data selection for pruning, leading to improved approximation accuracy.