Pairwise Correlation Coefficient

A Pairwise Correlation Coefficient is a correlation coefficient of paired data.

• Example(s):
  • a Pairwise Pearson Correlation Coefficient estimate for paired data $\{x,y\}$ such as: $\rho_{xy}=\dfrac{\sigma_{xy}}{\sigma_x\sigma_y}$,
  • a Pairwise Spearman Correlation Coefficient,
  • …
• Counter-Example(s)/:
  • Average Pairwise Spearman Correlation Coefficient,
  • Average Pairwise Pearson Correlation Coefficient.
• See: Pairwise Correlation Matrix, Pearson Correlation, Spearman Correlation, Covariance, Variance.

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References

2021

• (Wetcher-Hendricks, 2021) ⇒ Debra Wetcher-Hendricks (2021). "Correcting the Correction: A Revised Formula to Estimate Partial Correlations between True Scores". In: MDPI Psych, 3(1), 19-24.
  • QUOTE: This formula is one of many commonly used to calculate pairwise correlation coefficients.
    $\rho_{XY}=\dfrac{\sigma_{XY}}{\sigma_X\sigma_Y}$

2018

• (Eslami & Saeed, 2018) ⇒ Taban Eslami, and Fahad Saeed (2018)."Fast-GPU-PCC: A GPU-Based Technique to Compute Pairwise Pearson’s Correlation Coefficients for Time Series Data—fMRI Study". In: MDPI High-throughput, 7(2), 11.
  • QUOTE: Figure 2 shows an example of these elements.

Figure 2: Space needed for computing correlation of first $B$ voxels with the rest of voxels. Pairwise correlation is computed by multiplying a matrix containing time series of $B$ voxels to a matrix containing time series of all voxels which results in a matrix containing $N×\times B$ elements. This matrix has $NB−B(B+1)/2$ distinct correlation coefficients that need to be extracted and stored in the resulting correlation array.

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