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Related Concept Videos

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.
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 time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
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...
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...

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Related Experiment Video

Updated: Jun 19, 2026

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data
04:57

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data

Published on: May 16, 2022

Laplacian linear discriminant analysis approach to unsupervised feature selection.

Satoshi Niijima1, Yasushi Okuno

  • 1Department of PharmacoInformatics, Center for Integrative Education of Pharmacy Frontier, Graduate School of Pharmaceutical Sciences, Kyoto University, 46-29 Yoshida Shimoadachi-cho, Sakyo-ku, Kyoto 606-8501, Japan. niijima@pharm.kyoto-u.ac.jp

IEEE/ACM Transactions on Computational Biology and Bioinformatics
|October 31, 2009
PubMed
Summary

This study introduces a novel unsupervised feature selection method, LLDA-RFE, for genomics and proteomics. LLDA-RFE effectively identifies important features in cancer microarray data, outperforming existing unsupervised and even some supervised methods.

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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Related Experiment Videos

Last Updated: Jun 19, 2026

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data
04:57

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data

Published on: May 16, 2022

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
07:35

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Area of Science:

  • Genomics and Proteomics
  • Bioinformatics
  • Computational Biology

Background:

  • Feature selection is crucial for biomarker discovery in high-dimensional omics data.
  • Supervised methods are well-established, but unsupervised approaches are less explored for exploratory analysis.
  • Existing unsupervised methods like Laplacian score and SVD-entropy have limitations.

Purpose of the Study:

  • To develop an effective unsupervised feature selection method for high-dimensional data.
  • To extend Laplacian linear discriminant analysis (LLDA) for unsupervised applications.
  • To propose and evaluate a novel algorithm for computing LLDA efficiently.

Main Methods:

  • Extension of Laplacian linear discriminant analysis (LLDA) to unsupervised cases.
  • Development of an efficient algorithm for LLDA computation, suitable for high dimensionality and small sample sizes.
  • Implementation of LLDA-based Recursive Feature Elimination (LLDA-RFE) for feature selection.

Main Results:

  • LLDA-RFE demonstrated superior performance compared to Laplacian score on cancer microarray datasets.
  • LLDA-RFE showed favorable results against SVD-entropy.
  • The proposed unsupervised method even outperformed the supervised Fisher score on certain datasets.

Conclusions:

  • LLDA-RFE is a powerful unsupervised feature selection technique for omics data analysis.
  • The method offers a viable alternative to supervised approaches, especially in exploratory settings.
  • This work advances unsupervised learning applications in genomics and proteomics.