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Related Concept Videos

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...
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...
Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
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...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...

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Related Experiment Videos

Linear regression for face recognition.

Imran Naseem1, Roberto Togneri, Mohammed Bennamoun

  • 1The University of Western Australia, Crawley, Australia. imran.naseem@ee.uwa.edu.au

IEEE Transactions on Pattern Analysis and Machine Intelligence
|July 7, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces Linear Regression Classification (LRC) for face identification, modeling images on linear subspaces. The novel approach excels, especially with occlusions, achieving top results for scarf occlusion challenges.

Related Experiment Videos

Area of Science:

  • Computer Vision
  • Pattern Recognition
  • Biometrics

Background:

  • Face identification is a critical task in biometrics and computer vision.
  • Traditional methods face challenges with variations in pose, illumination, and occlusion.

Purpose of the Study:

  • To propose a novel face identification algorithm based on linear regression.
  • To address the challenge of contiguous occlusions in face recognition.
  • To evaluate the proposed algorithm's performance against state-of-the-art methods.

Main Methods:

  • Formulating face identification as a linear regression problem.
  • Developing a linear model representing probe images using class-specific galleries.
  • Employing the least-squares method to solve the inverse problem and minimize reconstruction error.
  • Introducing a Modular Linear Regression Classification (LRC) approach with Distance-based Evidence Fusion (DEF) for occlusions.

Main Results:

  • The proposed Linear Regression Classification (LRC) algorithm demonstrates high efficacy.
  • Extensive evaluations on standard databases show competitive performance.
  • The Modular LRC with DEF achieves state-of-the-art results for scarf occlusion.

Conclusions:

  • Linear regression provides a robust framework for face identification.
  • The proposed LRC algorithm is effective and efficient for face recognition tasks.
  • The Modular LRC approach with DEF significantly improves performance under occlusion.