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

Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...

You might also read

Related Articles

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

Sort by
Same author

Author Correction: UKB-MDRMF: a multi-disease risk and multimorbidity framework based on UK biobank data.

Nature communications·2026
Same author

MyESL: A Software for Evolutionary Sparse Learning in Molecular Phylogenetics and Genomics.

Molecular biology and evolution·2025
Same author

Rhizosphere microbial diversity and functional roles in tea cultivars: insights from high-throughput sequencing and functional isolates.

Plant signaling & behavior·2025
Same author

LLaFS++: Few-Shot Image Segmentation With Large Language Models.

IEEE transactions on pattern analysis and machine intelligence·2025
Same author

CATI: A medical context-enhanced framework for diagnosis code assignment in the UK Biobank study.

Artificial intelligence in medicine·2025
Same author

UKB-MDRMF: a multi-disease risk and multimorbidity framework based on UK biobank data.

Nature communications·2025

Related Experiment Video

Updated: Jun 9, 2026

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

Canonical correlation analysis for multilabel classification: a least-squares formulation, extensions, and analysis.

Liang Sun1, Shuiwang Ji, Jieping Ye

  • 1Department of Computer Science and the Center for Evolutionary Medicine and Informatics (CEMI) of The Biodesign Institute, Arizona State University, Tempe, AZ 85287, USA. sun.liang@asu.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 25, 2010
PubMed
Summary
This summary is machine-generated.

Canonical Correlation Analysis (CCA) for multilabel data is shown to be a least-squares problem, enabling efficient scaling. New extensions, including sparse CCA, are proposed and validated on benchmark datasets.

More Related Videos

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

Related Experiment Videos

Last Updated: Jun 9, 2026

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

Area of Science:

  • Machine Learning
  • Statistical Analysis
  • Data Mining

Background:

  • Canonical Correlation Analysis (CCA) is a standard method for identifying correlations between two sets of variables.
  • CCA is often used for supervised dimensionality reduction, mapping data and class labels to a lower-dimensional space.
  • While CCA is a least-squares problem for binary classification, its extension to multilabel settings is not well-defined.

Purpose of the Study:

  • To demonstrate that CCA in the multilabel case can be formulated as a least-squares problem under mild conditions.
  • To develop efficient algorithms for large-scale CCA by leveraging least-squares solvers.
  • To introduce novel extensions of CCA, including sparse formulations and partial least squares.

Main Methods:

  • Formulating multilabel Canonical Correlation Analysis (CCA) as a least-squares problem.
  • Applying efficient least-squares algorithms for scalability to large datasets.
  • Developing sparse CCA using 1-norm regularization and extending to partial least squares.

Main Results:

  • Established an equivalence between multilabel CCA and least-squares problems for high-dimensional data.
  • Demonstrated that CCA projections are independent of regularization on the other variable set.
  • Validated the effectiveness and efficiency of proposed CCA extensions on benchmark multilabel datasets.

Conclusions:

  • Multilabel CCA can be efficiently solved using least-squares methods, enabling scalability.
  • The proposed CCA extensions, including sparse CCA, offer effective solutions for complex data.
  • The study provides new insights into the regularization effects within CCA frameworks.