再生核希尔伯特空间回归可有效地处理多元高维非线性的数据回归。数字人建模领域涉及人体相关的静态和动态数据描述，整个过程需要处理大量高维度非线性数据。故此研究专注于再生核希尔伯特空间回归方法中核降秩回归及高斯过程回归方法的拓展，并提出相关改进方法，以实现数字人建模中静态颅骨重构与动态运动压缩应用。具体工作内容为：提出流形核降秩回归方法，实现人体三维下颌骨重建，提高了重建任务精度；改进多任务高斯过程回归方法，用于人体运动建模和压缩，提高了三维骨架运动压缩率与重建精度；设计并实现了三维下颌骨重建及运动数据压缩重建系统。本文的主要创新点包括：
一、提出了面向Kendall形状空间的改进多元核降秩回归方法，首次构建了面向Kendall形状空间的流形核降秩回归模型，给出了算法的精确求解方式。Kendall形状空间能够将欧氏空间中数据离散表示为流形，基于流形表达实现非线性降维，通过流形核方法将数据从Kendall形状空间映射为希尔伯特空间，实现多元高维非线性数据的回归分析。该算法具有高精度、等距不变性和相似变换鲁棒性等特点。
二、针对三维颅骨模型，构建了流形核降秩回归与并行加速算法，实现了对缺失下颌骨的高效重建。构建三维下颌骨点云数据的Kendall形状空间表示，通过并行加速的流形核降秩回归算法构建颅骨间的内在联系，挖掘颅骨内在知识表达。构建的流形表达具有高维非线性的特点，流形核降秩回归算法能够有效挖掘颅骨形状间的内在相关性，并利用该相关性完成点云重建任务。该算法具有高效、高精度和高稳定性特点，在流形空间与欧氏空间上的误差率都超越已知SOTA模型，证明了算法的有效性。
三、面向高维非线性动态序列数据，利用深度核学习方法将多任务高斯过程与神经网络相结合，改进了多任务高斯过程回归，实现了三维人体骨架运动数据的压缩重建。多任务高斯过程模型可以对运动数据中的时间相干性进行建模，而加入的图卷积网络可以充分提取骨架数据关节点之间的拓扑关系，从而获得更适用于动作建模的数据表达。实验表明，提出的压缩算法具有高压缩率和低重建误差特性，适用于时序数据的处理任务。  
基于上述创新性研究，设计并实现了基于回归的数字人建模平台，实现了下颌骨点云重建与人体运动压缩重建工作。该系统具有便捷性，交互性与实时性等特点，经扩展可广泛应用于相关动静态数据建模与分析。

Reproducing Kernel Hilbert Space (RKHS) regression is a powerful method for nonlinear data regression in high-dimensional multivariate datasets. Digital human modeling involves processing large amounts of high-dimensional nonlinear data related to the human body, including both static and dynamic data. This article focuses on expanding the research of kernel reduced rank regression and Gaussian process regression methods in RKHS regression, proposing relevant improvements for static skull reconstruction and dynamic motion compression applications in digital human modeling. Specifically, this work proposes a manifold kernel reduced rank regression method for achieving three-dimensional reconstruction of the human mandible, improving reconstruction accuracy. Additionally, an improved multi-task Gaussian process regression method is presented for human motion modeling and compression, enhancing the compression rate and reconstruction accuracy of 3D skeleton motion. Finally, a 3D mandibular reconstruction and motion data compression reconstruction system is designed and implemented. The main innovations of this article include:
1. An improved multivariate kernel reduced rank regression method was proposed for Kendall shape space. Constructed the first manifold kernel reduced rank regression model for Kendall shape space, and providing an analytic expression for the algorithm. Kendall shapes space can discretize the data in Euclidean space into manifolds, achieving nonlinear dimensionality reduction based on manifold representation, and map data from Kendall shape space to Hilbert space through manifold kernel method to realize regression analysis of multivariate high-dimensional nonlinear data. The algorithm possesses characteristics such as high accuracy, isometry invariance, and similarity transformation robustness.
2. Constructed the manifold kernel reduced rank regression and parallel acceleration algorithm, which achieves efficient reconstruction of missing mandibles. By constructing the Kendall shape space representation of 3D mandibular point cloud data and using a parallel accelerated manifold kernel reduced rank regression algorithm, the intrinsic connections between skulls were modeled. The constructed manifold expression has the characteristic of high-dimensional nonlinearity, and the manifold kernel reduced rank regression algorithm can effectively mine the internal correlation between the skull shapes, and complete the point cloud reconstruction task based on these correlations. The algorithm is highly efficient, accurate, and stable, with error rates in both manifold space and Euclidean space surpassing those of known state-of-the-art models, demonstrating the effectiveness of the algorithm.
3. Aiming at high-dimensional nonlinear dynamic sequence data, a deep kernel learning method is used to combine multi-task Gaussian processes with neural networks, improving multi-task Gaussian process regression and achieving compressed reconstruction of 3D human skeleton motion data. The multi-task Gaussian process method can model the time coherence in the motion data, and the graph convolution network can fully extract the topological relationship between the joints of the skeleton data, so as to obtain a more suitable data representation for action modeling. Experiments show that proposed compression algorithm has high compression rate and low reconstruction error characteristics, and is suitable for processing temporal data tasks.
Based on the  above innovative research, a regression-based digital human modeling platform has been designed and implemented, achieving mandibular point cloud reconstruction and human motion compression restoration. The system is characterized by convenience, interactivity, and real-time performance, and can be widely applied to modeling and analysis of related dynamic and static data with further extensions.