This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details.(August 2018) (Learn how and when to remove this message)
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, 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;[1] other ways can be multiple factor analysis (MFA),[2][3] or the STATIS method.[4] The method was first published by J. C. Gower in 1975.[5]
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, 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 a pair of shape instances annotated by landmark points. GPA applies the Procrustes analysis 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.
^Meullenet, Jean-François; Xiong, Rui; Findlay, Christopher J, eds. (2007). Multivariate and Probabilistic Analyses of Sensory Science Problems. doi:10.1002/9780470277539. ISBN 9780470277539.
^Escofier, B.; Pagès, J. (1994). "Multiple factor analysis (AFMULT package)". Computational Statistics & Data Analysis. 18: 121–140. doi:10.1016/0167-9473(94)90135-X.
^ A comparison of GPA and MFA with sensory data is a chapter of the bookMFA is the core of a recent book: Pagès Jérôme (2014). Multiple Factor Analysis by Example Using R. Chapman & Hall/CRC The R Series London 272 p
^Lavit, C.; Escoufier, Y.; Sabatier, R.; Traissac, P. (1994). "The ACT (STATIS method)". Computational Statistics & Data Analysis. 18: 97–119. doi:10.1016/0167-9473(94)90134-1.
^Gower, J. C. (1975). "Generalized procrustes analysis". Psychometrika. 40: 33–51. doi:10.1007/BF02291478. hdl:10.1007/BF02291478. S2CID 122244491.
and 15 Related for: Generalized Procrustes analysis information
GeneralizedProcrustesanalysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys...
statistics, Procrustesanalysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes (Greek: Προκρούστης)...
tellings, if the guest proved too tall, Procrustes would amputate the excess length; if the guest was too short Procrustes would stretch them until they died;...
variables that were scaled, rotated, and translated during the generalizeprocrustesanalysis. The resulting principal component scores project the shape...
distribution Generalized normal distribution Generalized p-value Generalized Pareto distribution GeneralizedProcrustesanalysisGeneralized randomized...
the original shapes. These landmarks are aligned using the generalizedprocrustesanalysis, which minimizes the least squared error between the points...
as multivariate analysis of variance and multivariate regression, can be used to test statistical hypotheses about shape. Procrustes-based analyses have...
similar problem, with interesting applications in shape analysis, is the orthogonal Procrustes problem, which consists of finding an orthogonal matrix...
in Germany, Japan and the United States. Confirmatory factor analysis checked by Procrustes rotation was used to analyze the data, and again five factors...
and error control. Physics-informed DMD: Physics-informed DMD forms a Procrustes problem that restricts the family of admissible models to a matrix manifold...
orthogonal matrix Q nearest a given matrix M is related to the Orthogonal Procrustes problem. There are several different ways to get the unique solution,...
Wang, Chang; Sridhar Mahadevan (2008). Manifold Alignment using ProcrustesAnalysis (PDF). The 25th International Conference on Machine Learning.[permanent...
explain the origin of the Ethiosemitic languages at this time. An mtDNA analysis by Gandini et al. (2016) has produced additional evidence in support of...
Global Information