Bayesian Geodesic Regression on Riemannian Manifolds
This is an incremental improvement for researchers in computational anatomy and shape analysis, addressing overfitting and dimensionality selection in geodesic regression.
The paper tackles the problem of geodesic regression on Riemannian manifolds lacking automatic dimensionality selection, developing a Bayesian model (BGRM) that adds regularization and a prior to drive unnecessary tangent vectors to zero. It demonstrates effectiveness on synthetic and real data, reducing dimensionality and analyzing shape variations in human corpus callosum and mandible data.
Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model. To avoid the overfitting problem, we add a regularization term to control the effectiveness of the model. To automatically select the dimensionality, we develop a prior for the geodesic regression model, which can automatically select the number of relevant dimensions by driving unnecessary tangent vectors to zero. To show the validation of our model, we first apply it in the 3D synthetic sphere and 2D pentagon data. We then demonstrate the effectiveness of our model in reducing the dimensionality and analyzing shape variations of human corpus callosum and mandible data.