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Related Concept Videos

Coefficient of Correlation01:12

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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.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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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.
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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...
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Sufficient Canonical Correlation Analysis.

Yiwen Guo, Xiaoqing Ding, Changsong Liu

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |April 13, 2016
    PubMed
    Summary
    This summary is machine-generated.

    Canonical Correlation Analysis (CCA) often overfits. This study introduces Sufficient CCA (S-CCA), inspired by sufficient dimension reduction theory, to effectively mitigate overfitting in joint dimension reduction tasks.

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    Area of Science:

    • Machine Learning
    • Computer Vision
    • Statistical Analysis

    Background:

    • Canonical Correlation Analysis (CCA) is a joint dimension reduction technique widely used in image processing and computer vision.
    • Traditional CCA is prone to overfitting in practical applications, limiting its effectiveness.
    • Overfitting hinders the performance of CCA in real-world scenarios.

    Purpose of the Study:

    • To address the overfitting issue in Canonical Correlation Analysis (CCA).
    • To introduce a novel method, Sufficient CCA (S-CCA), to improve CCA's robustness.
    • To enhance the performance of joint dimension reduction techniques.

    Main Methods:

    • Developed Sufficient CCA (S-CCA) based on sufficient dimension reduction theory.
    • Conducted theoretical analysis to validate the approach.
    • Performed experimental evaluations to compare S-CCA with existing methods.

    Main Results:

    • S-CCA effectively reduces overfitting in Canonical Correlation Analysis.
    • Theoretical and experimental results confirm the efficacy of S-CCA.
    • S-CCA demonstrates superior performance over popular CCA extensions, especially under severe overfitting conditions.

    Conclusions:

    • Sufficient CCA (S-CCA) offers a robust solution to the overfitting problem in Canonical Correlation Analysis.
    • The proposed S-CCA method enhances the reliability of joint dimension reduction.
    • S-CCA is a valuable advancement for applications sensitive to overfitting, such as in computer vision.