An equivalence relation between correspondence analysis and classical metric multidimensional scaling for the recovery of Euclidean distances

A theorem is proved showing that a special variant of correspondence analysis (CA), like classical two‐way metric multidimensional scaling (MMDS), recovers Euclidean distances (asymptotically, as a certain constant grows large) exactly, and in fact yields solutions equivalent up to a similarity transformation to MMDS, even in the case of ‘noisy’ data. Specifically, a slight modification of a use of CA for analysis of proximity data proposed independently by Gifi and by Weller & Romney, which depends on a certain additive constant, k , which should be ‘large’, is shown, as → ∞, to result in an R ‐dimensional solution equivalent, up to a scale factor, to that obtained by a certain form of MMDS. It is conjectured that this asymptotic result may account for the apparent success of the closely related ‘Gifi/Weller/Romney’ CA procedure in recovering multidimensional structure underlying proximity data.