Although correlation is often used as the linear relationship between two sets of points, I will in the following text use it more broadly to mean any relationship between two sets of points.
You have tasked yourself with finding the correlation between the different features in your dataset. Your purpose could be to remove highly correlated features or just improve your understanding of your data. Nonetheless, calculating and using the Pearson Correlation Coefficient (PCC) or the Spearman’s rank Correlation Coefficient (SCC) to get an overview of the correlations might be the first thing that comes to your mind.
Unfortunately, both of these are limited to linear (PCC) or monotonic (SCC) relationships. In datasets with many and complex features, many of them will be highly correlated, just not linearly (or monotonic). Instead these correlations can be non-linear which, as seen in the third row in the below figure, does not get detected with PCC.
