How to measure non linear relationship

Recently I’ve read a article regarding to the miss use of correlation coefficient to reveal the underlying relationship among several features. The author has demonstrated his own method, which has improved correlation coefficient method, to support better reveal of non linear relationship:

The article is at:

And his github repository is at:

My question is in Exploratory, how to find out non-linear relationship from large amount of features in a stragiforward way, like a co-matrix presented in the article: