Similarities and dissimilarities in classical multidimensional scaling I am having trouble reconciling between several terms in MDS.
According to [1], Section 14.8, Classical MDS takes similarities as inputs.
In [2], also cited in Wikipedia, Classical MDS takes dissimilarities as inputs. 
What is the agreed upon terminology?
[1] Hastie, T, R Tibshirani, and JH Friedman. The Elements of Statistical Learning. Springer, 2003.
[2] Borg, I., and P. J. F. Groenen. Modern Multidimensional Scaling: Theory and Applications. 2nd edition. New York: Springer, 2005.
 A: These two books are in full agreement.
Classical multidimensional scaling (where by "classical MDS" I understand Torgerson's MDS, following both Hastie et al. and Borg & Groenen) finds points $z_i$ such that their scalar products $\langle z_i, z_j \rangle$ approximate a given similarity matrix as well as possible. However, any dissimilarity matrix can be converted into a similarity matrix: dissimilarities are assumed to be Euclidean distances, from which centered scalar products can be computed and taken as similarities.
So the algorithm of classical/Torgerson MDS is as follows: $$\text{Euclidean distances}\to\text{Centered scalar products}\to\text{Optimal mapping},$$ i.e. $$\text{Dissimilarities}\to\text{Similarities}\to\text{Optimal mapping}.$$ What you consider an "input" here, does not really matter.
This is exactly what is written in Hastie et al.:

In classical scaling, we instead [as opposed to metric scaling in general] start with similarities [...]. This is attractive because there is an explicit
  solution in terms of eigenvectors [...]. If we have distances
  rather than inner-products, we can convert them to centered inner-products
  if the distances are Euclidean [...]. If the similarities are in fact centered inner-products, classical scaling is exactly equivalent to principal components [...]. Classical scaling is not equivalent to least squares scaling [that minimizes reconstruction of dissimilarities].

See my answer in What's the difference between principal components analysis and multidimensional scaling? for mathematical details.
