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 Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

250
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...
250
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

16.8K
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...
16.8K
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

3.5K
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...
3.5K
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

196
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
196
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

15.1K
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...
15.1K
Cartesian Vector Notation01:28

Cartesian Vector Notation

1.0K
Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
1.0K

You might also read

Related Articles

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

Sort by
Same author

Selective binding of phorbol esters and diacylglycerol by individual C1 domains of the PKD family.

The Biochemical journal·2007
Same author

[Investigation and analysis of China residents' environmental conservation desire].

Ying yong sheng tai xue bao = The journal of applied ecology·2007
Same author

[Analysis and identification of sea cucumber and products].

Guang pu xue yu guang pu fen xi = Guang pu·2007
Same author

Systematic identification of C. elegans miRISC proteins, miRNAs, and mRNA targets by their interactions with GW182 proteins AIN-1 and AIN-2.

Molecular cell·2007
Same author

HDAC inhibitor PCI-24781 decreases RAD51 expression and inhibits homologous recombination.

Proceedings of the National Academy of Sciences of the United States of America·2007
Same author

[Distribution and differentiation of marrow mesenchymal cells in tumor tissue: experimental with rabbits].

Zhonghua yi xue za zhi·2007
Same journal

Modeling the impact of budget limitation on the screening and treatment pathway of HPV-induced precancerous cervical lesions.

Mathematical biosciences and engineering : MBE·2026
Same journal

Modeling the effects of trait-mediated dispersal on coexistence of two species: Competition and non-consumptive predator-prey.

Mathematical biosciences and engineering : MBE·2026
Same journal

A close look at the viral reduction rate in target cell limited models.

Mathematical biosciences and engineering : MBE·2026
Same journal

A stochastic agent-based model for simulating tumor-immune dynamics and evaluating therapeutic strategies.

Mathematical biosciences and engineering : MBE·2026
Same journal

Addressing domain shift via imbalance-aware domain adaptation in embryo development assessment.

Mathematical biosciences and engineering : MBE·2026
Same journal

Effect of drug resistance on an HIV epidemic in heterogeneous populations.

Mathematical biosciences and engineering : MBE·2026
See all related articles

Related Experiment Video

Updated: Oct 4, 2025

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

5.8K

Data representation using robust nonnegative matrix factorization for edge computing.

Qing Yang1, Jun Chen1, Najla Al-Nabhan2

  • 1School of Computer Engineering, Nanjing Institute of Technology, Hongjing Avenue, Nanjing, China.

Mathematical Biosciences and Engineering : MBE
|February 9, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces robust constrained nonnegative matrix factorization (RCNMF), a new semi-supervised method that integrates local and global data structures for improved pattern recognition and edge computing applications.

Keywords:
1-normL2clusteringconstraint propagationedge computingnonnegative matrix factorization (NMF)

More Related Videos

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches
09:47

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

Published on: December 15, 2023

1.3K
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.8K

Related Experiment Videos

Last Updated: Oct 4, 2025

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

5.8K
Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches
09:47

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

Published on: December 15, 2023

1.3K
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.8K

Area of Science:

  • Data Science
  • Machine Learning
  • Artificial Intelligence

Background:

  • Nonnegative matrix factorization (NMF) is a key data representation technique used in edge computing, information retrieval, and pattern recognition.
  • Existing NMF algorithms struggle to incorporate both local and global data structures, and semi-supervised methods often overlook inter-class instance relationships.
  • This limits the effectiveness of NMF in learning robust and discriminative representations.

Purpose of the Study:

  • To propose a novel semi-supervised NMF approach, robust constrained nonnegative matrix factorization (RCNMF), for enhanced data representation.
  • To effectively integrate local and global data structures using graph regularization and constraint propagation.
  • To improve the learning of discriminative representations by considering relationships between instances of different classes.

Main Methods:

  • Developed RCNMF, a semi-supervised NMF approach combining L2,1-norm NMF and constraint propagation.
  • Incorporated joint graph regularization to leverage both local and global data structures, bringing similar class instances closer and dissimilar ones farther apart.
  • Utilized L2,1-norm cost function for noise and outlier robustness and applied L2,1-norm constraints for sparse representations.

Main Results:

  • The proposed RCNMF algorithm effectively learns robust and discriminative representations by integrating local and global data structures.
  • The method demonstrates superior performance compared to existing state-of-the-art algorithms in empirical experiments.
  • The convergence of the optimization algorithm used to solve the RCNMF framework is theoretically and empirically proven.

Conclusions:

  • RCNMF offers a significant advancement in semi-supervised nonnegative matrix factorization for applications like edge computing and pattern recognition.
  • The integration of graph regularization and constraint propagation leads to more robust and discriminative data representations.
  • The proposed method outperforms existing techniques, highlighting its potential for complex data analysis tasks.