With the Multi-way Correlation Coefficient, we can analyze the correlation between multiple variables in a dataset simultaneously. This is particularly useful in high-dimensional datasets where traditional pairwise correlation methods may not capture the relationships effectively.

Definition: Let $\text{mcor}(C)$ , the multi-way correlation coefficient, be

\text{mcor}(C) = \frac{1}{\sqrt{ d }} \sigma \{ \text{eigenvalues}(C) \},

where $\sigma$ is the Standard Deviation of a set of values, $d$ the dimension of the dataset and $C$ the matrix of computed Pearson Correlation Coefficients. (Taylor, 2020)

references

Taylor, B. M. (2020). A Multi-Way Correlation Coefficient. arXiv. https://doi.org/10.48550/arXiv.2003.02561