Unbalanced ANOVA for Testing Shape Variability in Statistical Shape Analysis

Title & Authors
Unbalanced ANOVA for Testing Shape Variability in Statistical Shape Analysis
Kim, Jong-Geon; Choi, Yong-Seok; Lee, Nae-Young;

Abstract
Measures are very useful tools for comparing the shape variability in statistical shape analysis. For examples, the Procrustes statistic(PS) is isolated measure, and the mean Procrustes statistic(MPS) and the root mean square measure(RMS) are overall measures. But these measures are very subjective, complicated and moreover these measures are not statistical for comparing the shape variability. Therefore we need to study some tests. It is well known that the Hotelling`s $\small{T^2}$ test is used for testing shape variability of two independent samples. And for testing shape variabilities of several independent samples, instead of the Hotelling`s $\small{T^2}$ test, one way analysis of variance(ANOVA) can be applied. In fact, this one way ANOVA is based on the balanced samples of equal size which is called as BANOVA. However, If we have unbalanced samples with unequal size, we can not use BANOVA. Therefore we propose the unbalanced analysis of variance(UNBANOVA) for testing shape variabilities of several independent samples of unequal size.
Keywords
Hotelling`s $\small{T^2}$ test;mean shape;shape variability;UNBANOVA;
Language
English
Cited by
1.
결측값이 있는 정준상관 행렬도의 형상변동 연구,홍현욱;최용석;신상민;강창완;

응용통계연구, 2010. vol.23. 5, pp.955-966
2.
자동차 환경내의 음성인식 자동 평가 플랫폼 연구,이성재;강선미;

한국통신학회논문지, 2012. vol.37. 7C, pp.538-543
1.
A Study of Automatic Evaluation Platform for Speech Recognition Engine in the Vehicle Environment, The Journal of Korean Institute of Communications and Information Sciences, 2012, 37, 7C, 538
References
1.
Choi, Y. S., Hyun, G. H. and Yun, W. J. (2005). Biplots variability based on the Procrustes analysis, Journal of the Korean Data Analysis Society, 7, 1925-1933.

2.
Dryden, I. L. and Mardia, K. V. (1998). Statistical Shape Analysis, John Wiley & Sons.

3.
Goodall, C. (1991). Prucrustes methods in the statistical analysis of shape(with discussion), Journal of Royal Statistical Society, Series B, 53, 285-339.

4.
Gower, J. C. (1975). Generalized Procrustes analysis, Psychometrika, 40, 33-50.

5.
Hyun, G. H. (2006). Resistant generalized Procrustes methods in shape analysis, Ph.D thesis, Pusan National University.

6.
Kendall, D. G. (1984). Procrustean metrics, and complex projective spaces, Bulletin of the London Mathematical Society, 16, 81-121.

7.
Kent, J. T. (1994). The complex Bingham distribution and shape analysis, Journal of Royal Statistical Society, Series B, 56, 285-299.

8.
Kim, J. G. (2009). A study on measures and tests for shape variability in statistical shape analysis, Ph.D thesis, Pusan National University.

9.
Mardia, K. V. and Dryden, I. L. (1989). The statistical analysis of shape data, Biometrika, 76, 271-281.

10.
Ten Berge, J. M. F. (1977). Orthogonal Procrustes rotation for two or more matrices, Psychometrika, 42, 267-276.