非线性高阶标记扩展
Nonlinear Higher-Order Label Spreading
摘要：
标签扩散是一种利用点云或网络数据进行半监督学习的通用技术，其可以被解释为标签在图上的扩散。虽然标签扩散有许多变体，但几乎所有都是线性模型，其中节点的传入信息是来自相邻节点的信息的加权和。在这里，我们通过图中高阶结构的非线性函数（即图中的三角形）将非线性添加到标签传播中。对于一类广泛的非线性函数，我们证明了我们的非线性高阶标签扩散算法收敛到一个约束半监督损失函数的全局解。我们证明了我们的方法在各种点云和网络数据集上的效率和功效，其中非线性高阶模型与经典的标签扩散以及超图模型和图神经网络相比毫不逊色。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
