Journal of Classification 3 DOI: 10.1007/s00357-017-9224-z On the Correspondence Between Procrustes Analysis and Bidimensional Regression Justin L. Kern University of Illinois at Urbana-Champaign Abstract: Procrustes analysis is defined as the problem of fitting a matrix of data to a target matrix as closely as possible (Gower and Dijksterhuis, 2004). The problem can take many forms, but the most common form, orthogonal Procrustes analysis, has as allowable transformations, a translation, a scaling, an orthogonal rotation, and a reflection. Procrustes analysis and other rotation methods have a long his- tory in quantitative psychology, as well as in other fields, such as biology (Siegel and Benson, 1982) and shape analysis (Kendall, 1984). In the field of quantitative geography, the use of bidimensional regression (Tobler, 1965) has recently become popular. Tobler (1994) defines bidimensional regression as “an extension of ordinary regression to the case in which both the independent and dependent variables are two-dimensional.” In this paper, it is established that orthogonal Procrustes analysis (without reflection) and Euclidean bidimensional regression are the same. As such, both areas of development can borrow from the other, allowing for a richer landscape of possibilities. Keywords: Procrustes analysis; Bidimensional regression. 1. Introduction Procrustes analysis has a long tradition in the field of psychometrics and quantitative psychology. The term “Procrustes analysis” comes from the Greek myth of Procrustes (Hurley and Cattell, 1962), wherein Procrustes invited strangers into his inn to sleep in his all-fitting bed. According to the tale, the bed was “all-fitting” because Procrustes fit his guests to the bed; he stretched his short guests with racks and chopped off the limbs of his tall Corresponding Author’s Address: J.L. Kern, Department of Psychology, University of Illinois, 603 East Daniel Street, Champaign, Illinois 61820, USA, e-mail: kern4@illinois. edu. Published onlin 4:35-48 (2017) e: 20 M rch 2017 a