Exploring the variability of DNA molecules via principal geodesic analysis on the shape space

H. Fotouhi and M. Golalizadeh

Journal of Applied Statistics, 2012, vol. 39, issue 10, 2199-2207

Abstract: Most of the linear statistics deal with data lying in a Euclidean space. However, there are many examples, such as DNA molecule topological structures, in which the initial or the transformed data lie in a non-Euclidean space. To get a measure of variability in these situations, the principal component analysis (PCA) is usually performed on a Euclidean tangent space as it cannot be directly implemented on a non-Euclidean space. Instead, principal geodesic analysis (PGA) is a new tool that provides a measure of variability for nonlinear statistics. In this paper, the performance of this new tool is compared with that of the PCA using a real data set representing a DNA molecular structure. It is shown that due to the nonlinearity of space, the PGA explains more variability of the data than the PCA.

Date: 2012
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DOI: 10.1080/02664763.2012.704353

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