I would like to execute multidimensional scaling (MDS) based on a matrix of Pearson correlation coefficients. The sklearn.manifold.MDS function takes a dissimilarity matrix as an input and I therefore need to convert my similarity matrix into a dissimilarity/distance matrix. What is the correct way of doing so?
According to this answer, a similarity matrix (S) can be converted to an euclidean distance matrix (d) via:
d = sqrt(2(1-S))
It also notes that on some occasions, the factor 2 can be omitted:
d = sqrt(1-S)
According to this paper (eq. 3.4) and this paper (eq. 3), the conversion should be done as follows:
d = 1-S
Which of those answers is correct, given that my similarity matrix has values between [-1,1] and the diagonal elements are 1 (it is symmetric)?
