Resistant GPA algorithms based on the M and LMS estimation

• Published in: Communications for statistical applications and methods Vol. 25; no. 6; pp. 673 - 685
• Main Authors: Hyun, Geehong, Lee, Bo-Hui, Choi, Yong-Seok
• Format: Journal Article
• Language: Korean
• Published: 한국통계학회 30.11.2018
• Subjects: generalized Procrustes analysis; least median of squares estimator; least squares; M-estimation; mean shape; resistant; shape analysis; mean shape; least squares; M-estimation; least median of squares estimator; resistant; shape analysis; generalized Procrustes analysis
• ISSN: 2287-7843

Procrustes analysis is a useful technique useful to measure, compare shape differences and estimate a mean shape for objects; however it is based on a least squares criterion and is affected by some outliers. Therefore, we propose two generalized Procrustes analysis methods based on M-estimation and least median of squares estimation that are resistant to object outliers. In addition, two algorithms are given for practical implementation. A simulation study and some examples are used to examine and compared the performances of the algorithms with the least square method. Moreover since these resistant GPA methods are available for higher dimensions, we need some methods to visualize the objects and mean shape effectively. Also since we have concentrated on resistant fitting methods without considering shape distributions, we wish to shape analysis not be sensitive to particular model.