Manifold-valued data: Learning, Registering and Clustering Shapes of Curves

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This paper introduces a shrinkage statistical model for analyzing, registering, and clustering multi-dimensional curves. The model utilizes reparametrization functions that act as local distributions on curves. Given the intricate nature of the model, we establish a connection with well-understood Riemannian manifolds. This connection enables us to simplify the reparametrization space and enhance the manageability of the optimization task. Moreover, we provide empirical evidence of the practical usefulness of our proposed method by applying it to a potential application involving the clustering of hominin cochlear shapes. Looking ahead, our research interests lie in developing theoretical extensions that can accommodate more complex spaces. By exploring new aspects of manifold learning and inference on high-dimensional manifolds, we aim to advance the field further.