Graph-based semi-supervised learning (SSL) has been widely investigated in recent works considering its powerful ability to naturally incorporate the diverse types of information and measurements. However, traditional graph-based SSL methods have cubic complexities and leading to low scalability. In this paper, we propose to perform graph-based SSL on mixture distribution components, named Mixture-distribution based Graph Smoothing (MGS), to address this challenge. Specifically, the intrinsic distributions of data are captured by a mixture density estimation model. A novel mixture-distribution based objective energy function is further proposed to incorporate few available annotations, which ensures the model complexity is irrelevant to the number of raw instances. The energy function can be simplified and effectively solved by viewing the instances and mixture components as the point clouds. Experiments on large datasets demonstrate the remarkable performance improvements and scalability of the proposed model, which proves the superiority of the MGS model.

考虑到基于图的半监督学习（SSL）能够自然地融合各种类型的信息和度量的强大功能，在最近的工作中对其进行了广泛的研究。但是，传统的基于图的SSL方法具有立方复杂性，导致可伸缩性较低。在本文中，我们建议对名为Mixture-distribution-based Graph Smoothing（MGS）的混合分布组件执行基于图的SSL，以解决这一挑战。具体而言，数据的固有分布是由混合密度估计模型捕获的。进一步提出了一种新颖的基于混合分布的目标能量函数，以合并少量可用的注释，从而确保模型的复杂性与原始实例的数量无关。通过将实例和混合分量视为点云，可以简化并有效解决能量函数。在大型数据集上进行的实验证明了所提出模型的显着性能改进和可扩展性，从而证明了MGS模型的优越性。