Multi-Way Correlation Coefficient

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

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. ¹