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

Distance Problem01:29

Distance Problem

When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
Dimensional Analysis01:27

Dimensional Analysis

Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
Dimensional Analysis03:40

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
Dimensional Analysis02:19

Dimensional Analysis

The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...

You might also read

Related Articles

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

Sort by
Same author

Holistic Invariant Retracing for Distortion-Resilient Multi-Modal Learning in Spatial Transcriptomics.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same author

Demonstration of efficient predictive surrogates for large-scale quantum processors.

Nature communications·2026
Same author

A DeepSeek-powered AI system for automated chest radiograph interpretation in clinical practice.

Nature communications·2026
Same author

NoisePO: Efficient Semantic Noise Generation and Ranking for Diffusion-Based Text-to-Image Synthesis.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same author

Stability and Generalization for Distributed SGDA.

IEEE transactions on pattern analysis and machine intelligence·2026
Same author

SPAgent: Adaptive Task Decomposition and Model Selection for General Video Generation and Editing.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Relation DETR+: Exploring Explicit Position Relation Prior for Dense Prediction.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

CAFE: Cross-View Adaptive Fusion and Cluster Center Enhancement for Robust Multi-View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

DIVER: Reinforced Diffusion Breaks Imitation Bottlenecks in End-to-End Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Ethics-Aware Safe Reinforcement Learning for Rare-Event Risk Control in Interactive Urban Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Learning Shape Anchors for Holistic Indoor Scene Understanding.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Video

Updated: Jun 3, 2026

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Max-min distance analysis by using sequential SDP relaxation for dimension reduction.

Wei Bian1, Dacheng Tao

  • 1Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, Australia. wei.bian@student.uts.edu.au

IEEE Transactions on Pattern Analysis and Machine Intelligence
|March 26, 2011
PubMed
Summary
This summary is machine-generated.

Max-min distance analysis (MMDA) is a new method for discriminative dimension reduction that maximizes the minimum distance between all class pairs. This approach enhances data separation for improved classification and visualization.

Related Experiment Videos

Last Updated: Jun 3, 2026

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Area of Science:

  • Machine Learning
  • Data Science
  • Computer Vision

Background:

  • Discriminative dimension reduction is crucial for pattern recognition.
  • Existing methods like Fisher's Linear Discriminant Analysis (FLDA) may not optimize all class pair separations.
  • There is a need for robust dimension reduction techniques that consider global class separability.

Purpose of the Study:

  • To introduce Max-Min Distance Analysis (MMDA) as a novel criterion for discriminative dimension reduction.
  • To extend MMDA to handle general data distributions using kernel methods (Kernel MMDA or KMMDA).
  • To develop an efficient algorithm for solving the optimization problem inherent in MMDA/KMMDA.

Main Methods:

  • MMDA maximizes the minimum pairwise distance between C classes in a low-dimensional subspace.
  • Kernel MMDA (KMMDA) extends the criterion for non-Gaussian or complex data distributions.
  • A sequential convex relaxation algorithm is proposed to solve the non-smooth max-min optimization problem with orthonormal constraints.

Main Results:

  • MMDA and KMMDA effectively consider the separation of all class pairs, unlike some traditional methods.
  • The proposed sequential convex relaxation algorithm provides an approximate solution to the optimization problem.
  • Experiments on synthetic and real datasets demonstrate the effectiveness of MMDA/KMMDA for classification and data visualization.

Conclusions:

  • MMDA offers a superior approach to discriminative dimension reduction by optimizing global class separation.
  • KMMDA provides a flexible extension for diverse data distributions.
  • The developed optimization algorithm enables practical application of MMDA/KMMDA, showing promising results in empirical evaluations.