Exploring the variability of DNA molecules via principal geodesic analysis on the shape space |
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Authors: | H Fotouhi |
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Institution: | Department of Statistics, Faculty of Mathematical Sciences , Tarbiat Modares University , PO Box 14115-134, Tehran , Iran |
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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. |
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Keywords: | nonlinear statistics statistical shape analysis DNA modeling principal component analysis principal geodesic analysis |
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