Advanced shape analysis studies such as regression and classification need to be performed on curved manifolds, where often, there is a lack of standard statistical formulations. To overcome these limitations, we introduce a novel machine-learning method on the shape space of curves that avoids direct inference on infinite-dimensional spaces and instead performs Bayesian inference with spherical Gaussian processes decomposition. As an application, we study the shape of the cochlear spiral-shaped cavity within the petrous part of the temporal bone. This problem is particularly challenging due to the relationship between shape and gender, especially in children. Experimental results for both synthetic and real data show improved performance compared to state-of-the-art methods.

One of the challenging classification problems consists of learning relevant and meaningful relationships between high dimensional representations across a relatively few observed individuals. Since this problem could have drastic effects on the classification performance, we propose a Bayesian alternative in the case of logistic regression. The proposed method has the additional benefit to learn both the adaptive embedding, as a Gaussian process, and the dimensionality reduction, jointly within the same Bayesian framework. We illustrate the efficiency and the accuracy of our framework for classifying images of manufacturing defects.