I'm looking for a method to calculate the similarity between two distance matrices. I have two distance matrices that represents some X-data and another that represents Y-data and my goal is to see which X-data that is most similar to the Y-data. I could do something like a PLS with multi-Y, but I don't want to influence the X-data matrixes.

What I have is cross-reactivity data for a set of proteins and ligands. One of the X-distance matrixes consists of sequence homologies between the proteins and the Y-matrix will contain the distances derived from a PCA describing the ligand activities. I want to test another way of calculating the protein similarities and see if that measure is more correlated to the ligand activities. In the end, my goal is to take a new protein sequence, run it through the model and get suggestions on likely ligands.

*Imported from: http://blueobelisk.stackexchange.com/questions/286*

I guess the matrices are not of equal dimensions?

Yes, the distance matrixes are of equal dimensions.