# Is the Normalized Information Distance (NID) a euclidean distance?

I'm trying to determine if I can plot my dissimilarity matrix (which is a Normalized Information Distance / the "Universal Distance Metric" dissimilarity matrix), in a lower-dimensional space using PCA or MDS (see Wikipedia article here if you are not familiar: https://en.wikipedia.org/wiki/Normalized_compression_distance).

I'm having a hard time determining if the Universal Distance metric / Normalized Information Distance is a "Euclidean" distance, which is required for PCA, and not necessary required for MDS (see this post: What's the difference between principal component analysis and multidimensional scaling?).

Also, the equivalent R functions to do a PCA reduction in R is prcomp(dissimilarityMatrix), and for mds is cmdscale(dissimilarityMatrix, eig=?, k=3). I assume if eig=TRUE, the MDS returns the same coordinates as prcomp, but if it's FALSE, then it differs?

• Could you be more specific about the sense in which a Euclidean distance is "required for PCA"? Ordinarily, PCA is conducted as a decomposition of an arbitrary matrix and as such seems to have no such requirements. – whuber Jun 29 '17 at 19:01
• I am referring to the second post I linked to in my post - see "amoeba"'s response. – areyoujokingme Jul 5 '17 at 18:50