Dimensionality reduction to correlate large number of variables
Yes, in scikit-learn, you can find the correlation between the elements using LedoitWolf Estimator. For dimensionality reduction, I assume you will use PCA but then, you want to backtrack the reduced to the original data, for that I don't have a solution, since, PCA transforms your data and computes the largest variance direction. But, yes both of these won't require any labels.