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

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.4K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.4K
Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

29.6K
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
29.6K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.5K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
18.5K
Vectors01:30

Vectors

631
Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
631
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

593
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
593
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

689
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment....
689

You might also read

Related Articles

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

Sort by
Same author

Federated learning with noisy labels: A comprehensive and concise review of current methodologies and future directions.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Hyperbolic Self-Paced Multi-Expert Network for Cross-Domain Few-Shot Facial Expression Recognition.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2025
Same author

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images.

Computers in biology and medicine·2024
Same author

DeGCN: Deformable Graph Convolutional Networks for Skeleton-Based Action Recognition.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2024
Same author

Relationship-Guided Knowledge Transfer for Class-Incremental Facial Expression Recognition.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2024
Same author

Knowledge Distillation Meets Label Noise Learning: Ambiguity-Guided Mutual Label Refinery.

IEEE transactions on neural networks and learning systems·2023
Same journal

Granular Ball-Based Noise-Resistant Fuzzy Multineighborhood Feature Selection via Label Enhancement and Feature Graph.

IEEE transactions on neural networks and learning systems·2026
Same journal

Fighting Evolving Spam With ARTMAP Models: A Noise-Resilient Online Detection Framework.

IEEE transactions on neural networks and learning systems·2026
Same journal

HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems.

IEEE transactions on neural networks and learning systems·2026
Same journal

Negation of Basic Belief Assignment in Multisource Information Fusion on Dempster-Shafer Theory With Applications in Pattern Classification.

IEEE transactions on neural networks and learning systems·2026
Same journal

Intervention Feasible Region and Driver Risk Capacity Aware Human-Machine Collaborative Safe Trajectory Planning.

IEEE transactions on neural networks and learning systems·2026
Same journal

A Unified Differential Denoising Learning Framework With a Pre-Trained Model and Fuzzy Graph Networks for Drug-Drug Interaction Prediction.

IEEE transactions on neural networks and learning systems·2026
See all related articles

Related Experiment Video

Updated: Mar 12, 2026

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.4K

Decorrelation of Neutral Vector Variables: Theory and Applications.

Zhanyu Ma, Jing-Hao Xue, Arne Leijon

    IEEE Transactions on Neural Networks and Learning Systems
    |November 12, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces novel nonlinear transformations for decorrelating neutral vector variables, enabling the creation of mutually independent scalar variables even for non-Gaussian data. These methods outperform traditional techniques for enhanced data analysis.

    More Related Videos

    Modeling the Functional Network for Spatial Navigation in the Human Brain
    05:55

    Modeling the Functional Network for Spatial Navigation in the Human Brain

    Published on: October 13, 2023

    1.6K
    Decoding Natural Behavior from Neuroethological Embedding
    08:00

    Decoding Natural Behavior from Neuroethological Embedding

    Published on: October 3, 2025

    833

    Related Experiment Videos

    Last Updated: Mar 12, 2026

    Basics of Multivariate Analysis in Neuroimaging Data
    06:35

    Basics of Multivariate Analysis in Neuroimaging Data

    Published on: July 24, 2010

    17.4K
    Modeling the Functional Network for Spatial Navigation in the Human Brain
    05:55

    Modeling the Functional Network for Spatial Navigation in the Human Brain

    Published on: October 13, 2023

    1.6K
    Decoding Natural Behavior from Neuroethological Embedding
    08:00

    Decoding Natural Behavior from Neuroethological Embedding

    Published on: October 3, 2025

    833

    Area of Science:

    • Statistics
    • Data Analysis
    • Information Theory

    Background:

    • Conventional principal component analysis (PCA) fails to achieve mutual independence for non-multivariate-Gaussian distributed neutral vector variables.
    • Decorrelation is crucial for simplifying complex datasets and improving downstream analysis.

    Purpose of the Study:

    • To propose and evaluate novel invertible nonlinear transformations for decorrelating neutral vector variables.
    • To achieve mutual independence of scalar variables from non-Gaussian neutral vectors.

    Main Methods:

    • Development of two fundamental invertible transformations: serial nonlinear transformation and parallel nonlinear transformation.
    • Application of these transformations to neutral vector variables, including those from Dirichlet and mixture of Dirichlet distributions.
    • Verification of mutual independence using distance correlation measurements.

    Main Results:

    • The proposed transformations successfully decorrelate highly negatively correlated neutral vectors into mutually independent scalar variables.
    • The transformed variables retain the same degrees of freedom as the original vector.
    • Demonstrated effectiveness on synthesized data and in practical applications.

    Conclusions:

    • The novel nonlinear transformation strategies provide an effective method for achieving mutual independence in decorrelated neutral vector variables.
    • These methods offer advantages over conventional techniques, particularly for non-Gaussian data distributions.