Generalized Procrustes analysis (GPA) is a method of
statistical analysis
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
that can be used to compare the shapes of objects, or the results of surveys, interviews, or panels. It was developed for analysing the results of
free-choice profiling, a survey technique which allows respondents (such as
sensory panelists) to describe a range of products in their own words or language. GPA is one way to make sense of free-choice profiling data; other ways can be
multiple factor analysis (MFA), or the STATIS method. The method was first published by J. C. Gower in 1975.
Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, generating a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a
principal component analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
, GPA uses individual level data and a measure of variance is utilized in the analysis.
The
Procrustes distance provides a metric to minimize in order to
superimpose
Superimposition is the placement of one thing over another, typically so that both are still evident.
Graphics
In graphics, superimposition is the placement of an image or video on top of an already-existing image or video, usually to add to t ...
a pair of shape instances annotated by
landmark point
In morphometrics, landmark point or shortly landmark is a point in a shape object in which correspondences between and within the populations of the object are preserved. In other disciplines, landmarks may be known as vertices, anchor points, co ...
s. GPA applies the
Procrustes analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name ''Procrustes'' ( el, Προκρούστης) refers to a bandit from Greek mythology who made his victims fi ...
method to superimpose a population of shapes instead of only two shape instances.
The algorithm outline is the following:
# arbitrarily choose a reference shape (typically by selecting it among the available instances)
# superimpose all instances to current reference shape
# compute the mean shape of the current set of superimposed shapes
# if the Procrustes distance between the mean shape and the reference is above a certain threshold, set the reference to mean shape and continue to step 2.
See also
*
Procrustes analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name ''Procrustes'' ( el, Προκρούστης) refers to a bandit from Greek mythology who made his victims fi ...
*
Orthogonal Procrustes problem The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A and B and asked to find an orthogonal matrix \Omega which most closely maps A to B. Specifically,
:R = \arg\m ...
References
* {{cite book, author=I.L. Dryden and K.V. Mardia, title=Statistical Shape Analysis, publisher=John Wiley & Sons, year=1998, isbn=0-471-95816-6
Multivariate statistics
Euclidean symmetries
Biometrics