Speaker
Description
Object oriented data analysis (OODA) provides a framework for the statistical analysis of a wide variety of highly structured data. Shapes, images, functions, covariance matrices, networks and other manifold-valued data are all examples of object data that can be analyzed using OODA methods. Shapes of 3D objects are a type of manifold-valued data, invariant to translation, rotation and scale. It is often of interest to summarize the dynamic evolution of object shapes in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres (PNS) gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the PNS methodology to 3D subshape spaces and provide some practical fitting algorithms. Further relevant approaches include smoothing splines on manifolds. The methodology is applied to placenta shape change, a sliding clamp multi-protein complex, and dynamic peptide analysis.