Anisotropic generalized Procrustes analysis

Generalized Procrustes analysis is a popular method for matching several configurations by translations, rotations/reflections and scaling constants. It aims at producing a group average from these Euclidean similarity transformations followed by bi-linear approximation of this group average for graphical inspection. An extension that allows for anisotropic scaling (i.e. different scaling of different dimensions) is proposed. This method is illustrated using two real data sets from sensory analysis.

[1]  Fabio Crosilla,et al.  Use of generalised Procrustes analysis for the photogrammetric block adjustment by independent models , 2002 .

[2]  Maurizio Vichi,et al.  Data Analysis, Classification and the Forward Search , 2006 .

[3]  Jan Kmenta,et al.  A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models , 1974 .

[4]  Anthony A. Williams,et al.  The use of free-choice profiling for the evaluation of commercial ports , 1984 .

[5]  Ingwer Borg,et al.  A direct approach to individual differences scaling using increasingly complex transformations , 1978 .

[6]  Edmund R. Peay,et al.  Multidimensional rotation and scaling of configurations to optimal agreement , 1988 .

[7]  J. Berge,et al.  Orthogonal procrustes rotation for two or more matrices , 1977 .

[8]  Mohammed Bennani Dosse,et al.  Anisotropic Orthogonal Procrustes Analysis , 2010, J. Classif..

[9]  Fabio Crosilla,et al.  A Forward Search Method for Robust Generalised Procrustes Analysis , 2006 .

[10]  M. Akca.  GENERALIZED PROCRUSTES ANALYSIS AND ITS APPLICATIONS IN PHOTOGRAMMETRY , 2003 .

[11]  J. Gower,et al.  The interpretation of Generalized Procrustes Analysis and allied methods , 1991 .

[12]  Garmt Dijksterhuis,et al.  Interpreting generalized procrustes analysis 'analysis of variance' tables , 1990 .

[13]  Dirk L. Knol,et al.  Orthogonal rotations to maximal agreement for two or more matrices of different column orders , 1984 .

[14]  P. Arabie,et al.  Three-Way Scaling and Clustering. , 1991 .

[15]  S. R. Searle,et al.  The Vec-Permutation Matrix, the Vec Operator and Kronecker Products: A Review , 1981 .

[16]  C. Goodall.  Procrustes methods in the statistical analysis of shape , 1991 .

[17]  S. Lauritzen,et al.  Globally convergent algorithms for maximizing a likelihood function , 1991 .

[18]  B. Green.  THE ORTHOGONAL APPROXIMATION OF AN OBLIQUE STRUCTURE IN FACTOR ANALYSIS , 1952 .

[19]  I. Borg,et al.  Geometric Representations of Relational Data , 1981 .

[20]  J. Piggott.  Statistical procedures in food research , 1986 .

[21]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .