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Related Concept Videos

Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
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...
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.
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...
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...
Extraction: Advanced Methods00:56

Extraction: Advanced Methods

Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is formed in...

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Related Experiment Videos

Efficient sparse kernel feature extraction based on partial least squares.

Charanpal Dhanjal1, Steve R Gunn, John Shawe-Taylor

  • 1University of Southampton, Southampton, UK. cd04r@ecs.soton.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 23, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a general framework for feature extraction using Partial Least Squares, yielding new Sparse Maximal Alignment (SMA) and Sparse Maximal Covariance (SMC) methods. These methods offer efficient, scalable solutions for machine learning tasks with irrelevant features.

Related Experiment Videos

Area of Science:

  • Machine Learning
  • Data Science
  • Computer Science

Background:

  • Irrelevant features in training data pose a significant challenge for machine learning.
  • Feature extraction is crucial, with methods often chosen based on the inference algorithm.

Purpose of the Study:

  • To formalize a general framework for feature extraction based on Partial Least Squares.
  • To introduce two new sparse kernel feature extraction methods: Sparse Maximal Alignment (SMA) and Sparse Maximal Covariance (SMC).

Main Methods:

  • Developed a general framework for feature extraction using Partial Least Squares with user-defined criteria for projection directions.
  • Derived Sparse Maximal Alignment (SMA) and Sparse Maximal Covariance (SMC) methods within this framework.
  • Demonstrated linear scaling in training time with the number of examples and efficient projection of new examples.

Main Results:

  • SMA and SMC extract features that are as predictive as those from popular existing methods.
  • On large text retrieval and face detection datasets, SMA and SMC match the performance of original features with Support Vector Machines.
  • The new methods offer simple implementation and efficient computation.

Conclusions:

  • The proposed framework unifies existing results and offers new insights into feature extraction.
  • SMA and SMC provide effective and computationally efficient solutions for handling irrelevant features in machine learning.
  • These methods demonstrate strong performance on real-world datasets, particularly in text retrieval and face detection.