Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

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...
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...
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.
Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

[Clinical diagnostic value of procalcitonin detection in local infection and sepsis].

Nan fang yi ke da xue xue bao = Journal of Southern Medical Universityยท2010
Same author

Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration.

Optics lettersยท2010
Same author

[Construction of DNA vaccine pcDNA3.1(+)/tetraspanin 2-A against Schistosoma japonicum and its immune-protective effect in mice].

Zhongguo ji sheng chong xue yu ji sheng chong bing za zhi = Chinese journal of parasitology & parasitic diseasesยท2010
Same author

Fluorescence-enhanced organogels and mesomorphic superstructure based on hydrazine derivatives.

Langmuir : the ACS journal of surfaces and colloidsยท2010
Same author

Cancer-derived mutations in the fibronectin III repeats of PTPRT/PTPrho inhibit cell-cell aggregation.

Cell communication & adhesionยท2010
Same author

Simulation of wavelength conversion based on integrated saturable absorber.

Applied opticsยท2010
Same journal

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

IEEE transactions on neural networksยท2013
Same journal

Guest editorial: special section on white box nonlinear prediction models.

IEEE transactions on neural networksยท2011
Same journal

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

IEEE transactions on neural networksยท2011
Same journal

Guest editorial: special section on data-based control, modeling, and optimization.

IEEE transactions on neural networksยท2011
Same journal

Neural network-based multiple robot simultaneous localization and mapping.

IEEE transactions on neural networksยท2011
Same journal

Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems.

IEEE transactions on neural networksยท2011
See all related articles

Related Experiment Video

Updated: Jun 26, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Nonlinear dimensionality reduction by locally linear inlaying.

Yuexian Hou1, Peng Zhang, Xingxing Xu

  • 1School of Computer Science and Technology, Tianjin University, Tianjin 300072, China. yxhou@tju.edu.cn

IEEE Transactions on Neural Networks
|January 20, 2009
PubMed
Summary
This summary is machine-generated.

A new algorithm called locally linear inlaying (LLI) efficiently discovers low-dimensional structures in high-dimensional data. LLI is robust to noise and handles uneven data distributions, offering improved manifold learning.

More Related Videos

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Related Experiment Videos

Last Updated: Jun 26, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

  • Data Science
  • Machine Learning
  • Computational Geometry

Background:

  • High-dimensional data is prevalent in information processing.
  • Intrinsic low-dimensional structures often exist within this data.
  • Manifold learning algorithms aim to uncover these underlying structures.

Purpose of the Study:

  • Introduce a novel manifold learning algorithm, locally linear inlaying (LLI).
  • Address limitations of existing methods in efficiency, data distribution handling, and noise robustness.
  • Provide quantitative evaluation criteria for embedding results.

Main Methods:

  • Developed the locally linear inlaying (LLI) algorithm.
  • Employed a divide-and-conquer strategy for efficient computation.
  • Proposed information theory and Kolmogorov complexity-based criteria for evaluation.

Main Results:

  • LLI exhibits linear time complexity, making it efficient.
  • The algorithm effectively handles non-uniform sample distributions.
  • LLI demonstrates robustness to noise, outperforming Isomap, LTSA, and LLC.
  • Demonstrated effectiveness on both synthetic and real-world datasets.

Conclusions:

  • Locally linear inlaying (LLI) is an efficient and robust manifold learning algorithm.
  • LLI offers significant advantages over existing methods for discovering low-dimensional structures.
  • The proposed evaluation criteria provide quantitative measures for embedding quality.