论文标题
非线性高阶标签扩展
Nonlinear Higher-Order Label Spreading
论文作者
论文摘要
标签扩展是使用点云或网络数据半监督学习的一般技术，可以将其解释为图上标签的扩散。尽管有许多标签扩展的变体，但几乎所有标签传播都是线性模型，其中传入节点的信息是来自相邻节点的加权信息。在这里，我们在图中通过高阶结构的非线性函数（即图中的三角形）添加了非线性。对于广泛的非线性函数，我们证明了非线性高阶标签扩展算法的收敛到约束半监督损耗函数的全局解决方案。我们证明了我们方法在各种点云和网络数据集上的效率和功效，在这些点云和网络数据集上，非线性高阶模型与经典标签扩展以及超图形模型和图形神经网络相比有利。
Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are many variants of label spreading, nearly all of them are linear models, where the incoming information to a node is a weighted sum of information from neighboring nodes. Here, we add nonlinearity to label spreading through nonlinear functions of higher-order structure in the graph, namely triangles in the graph. For a broad class of nonlinear functions, we prove convergence of our nonlinear higher-order label spreading algorithm to the global solution of a constrained semi-supervised loss function. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the nonlinear higher-order model compares favorably to classical label spreading, as well as hypergraph models and graph neural networks.
