CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

of zeros (Wu et al., 2002). The “goodness-of-fit” criterion for matrix to match
is provided by the sum of squared errors as presented in Equation 20. The value of
measures the degree of dissimilarity between the two matrices after
rotational and scaling effects have been applied. In this state, the shapes have become
as similar as possible.
Equation 20 Procrustes Analysis rotation criterion
‖
‖
Procrustes Analysis is an asymmetric method and its outcome depends solely on the
choice of the reference object. Generally
Equation 21 Procrustes Analysis asymmetric dissimilarities
4.2.3 Generalised Procrustes Analysis
Generalised Procrustes Analysis (GPA) (Gower, 1975; Gower, 2010) is performed in
cases where matrices , with , need to be simultaneously
transformed and matched against each other without any specific order. An intuitive
initial approach would be to examine and evaluate all pair combinations of the initial
shapes by calculating the dissimilarity measures using the mathematical type of
Equation 20. In this case, the sum of all dissimilarity measures could be presented as
∑‖
‖
Equation 22 Procrustes rotation criterion in GPA
However, this approach results once more to asymmetry based on Equation 21. Thus,
the idea of a single target matrix requires reconsideration (Gower, 2010). GPA was
introduced in order to find a group average configuration (Dijksterhuis and Gower,
1992; Dijksterhuis, 1994) or consensus (Gower, 1975), to which the individual
subspaces are compared simultaneously (Figure 4-2). This new approach provides
greater homogeneity and, in contrast to ordinary Procrustes Analysis, GPA is indeed a
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