Generalized Procrustes analysis
Encyclopedia
Generalized Procrustes analysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys, interviews, panels. It was developed for analyising 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 the only way to make sense of free-choice profiling data (Meullenet et al., 2007).
Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, thus it generates a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a principal component analysis, since GPA uses individual level data, a measure of variance is utilized in the analysis.
The Procrustes distance provides a metric to minimize in order to superimpose a pair of shape instances annotated by landmark point
s. GPA applies the Procrustes analysis
method to superimpose a population of shapes instead of only two shape instances.
The algorithm outline is the following:
Sensory analysis
Sensory analysis is a scientific discipline that applies principles of experimental design and statistical analysis to the use of human senses for the purposes of evaluating consumer products. The discipline requires panels of human assessors, on whom the products are tested, and recording the...
) to describe a range of products in their own words or language. GPA is the only way to make sense of free-choice profiling data (Meullenet et al., 2007).
Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, thus it generates a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a principal component analysis, since GPA uses individual level data, a measure of variance is utilized in the analysis.
The Procrustes distance provides a metric to minimize in order to superimpose a pair of shape instances annotated by landmark point
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, control points, sites, profile points, 'sampling'...
s. GPA applies the Procrustes analysis
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 refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.To compare the shape of...
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 threshold, set reference to mean shape and continue to step 2.