论文标题
Riemannian歧管上的贝叶斯大地测量回归
Bayesian Geodesic Regression on Riemannian Manifolds
论文作者
论文摘要
已经提出了用于拟合大地曲线的大地回归。但是，它不能自动选择数据的维度。在本文中，我们在Riemannian歧管（BGRM）模型上开发了贝叶斯大地测试模型。为了避免过度拟合问题，我们添加了一个正规化术语来控制模型的有效性。为了自动选择维度，我们为地理回归模型开发了一个先验，该模型可以自动选择相关维数的数量，通过将不必要的切线向量驱动到零。为了显示我们模型的验证，我们首先将其应用于3D合成球和2D五角大楼数据。然后，我们证明了模型在降低人体call体和下颌骨数据的形状变化方面的有效性。
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.
