Cosine-like alternative to Mahalanobis distance

I would like to have a distance measure that takes into account how spread are vectors in a dataset, to weight the absolute distance from one point to another. The Mahalanobis distance does exactly this, but it is a generalization of Euclidean distance, which is not particularly suitable for high-dimensional spaces (see for instance here).

Do you know of any measure that is suitable in high-dimensional spaces while also taking into account the correlation between datapoints?

Thank you! :)