黎曼流形上的广义部分线性模型
Generalized partially linear models on Riemannian manifolds
摘要：
介绍了黎曼流形上的广义部分线性模型。这些模型，像普通的广义线性模型一样，是黎曼流形上的部分线性模型的推广，允许响应变量具有不同于正态分布的误差分布模型。部分线性模型在模型的某些协变量是黎曼流形的元素时特别有用，因为这些空间的曲率使得很难定义参数模型。该模型的开发是为了解决一个有趣的应用程序，预测儿童的服装适合他们的身体的3D扫描的基础上。出于这个原因，我们专注于逻辑和顺序模型和重要和困难的情况下，黎曼流形是三维情况下的肯德尔的形状空间。一个著名的3D数据库进行了实验研究，以检查该程序的良好性。最后，它适用于从西班牙儿童人口的人体测量调查获得的3D数据库。与相关技术进行了比较研究。
英文摘要：
The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application, the prediction of children's garment fit based on 3D scanning of their body. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three-dimensional case of Kendall's shape space. An experimental study with a well-known 3D database is carried out to check the goodness of the procedure. Finally it is applied to a 3D database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.
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