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arXiv 2103.14867cs.LGcs.SIphysics.data-an
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超图上半监督学习的非线性扩散方法

A nonlinear diffusion method for semi-supervised learning on hypergraphs

School of Computer Science(计算机科学学院);Gran Sasso Science Institute(大萨索科学研究所);Department of Computer Science(计算机科学系);Cornell University(康奈尔大学);School of Mathematics(数学学院)

Francesco Tudisco, Konstantin Prokopchik, Austin R. Benson

摘要:

超图是数据中多路关系的常见模型,超图半监督学习是将标签分配给超图中的所有节点的问题,仅在少数节点上给出标签。扩散和标签扩散是图环境中半监督学习的经典技术,并且有一些标准的方法将它们扩展到超图。然而,这些方法都是线性模型,并没有提供一个明显的方法来结合节点特征进行预测。在这里,我们在超图上开发了一个非线性扩散过程,该过程根据超图结构传播特征和标签,这可以被解释为超图平衡网络。即使这个过程是非线性的,我们表现出全局收敛到一个独特的限制点的广泛的非线性,这是一个可解释的,正规化的半监督学习损失函数的全局最优。极限点作为一个节点嵌入,我们从这个节点嵌入中使用线性模型进行预测。我们的方法比几个超图神经网络更准确,也需要更少的时间来训练。

英文摘要:

Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are classical techniques for semi-supervised learning in the graph setting, and there are some standard ways to extend them to hypergraphs. However, these methods are linear models, and do not offer an obvious way of incorporating node features for making predictions. Here, we develop a nonlinear diffusion process on hypergraphs that spreads both features and labels following the hypergraph structure, which can be interpreted as a hypergraph equilibrium network. Even though the process is nonlinear, we show global convergence to a unique limiting point for a broad class of nonlinearities, which is the global optimum of a interpretable, regularized semi-supervised learning loss function. The limiting point serves as a node embedding from which we make predictions with a linear model. Our approach is much more accurate than several hypergraph neural networks, and also takes less time to train.

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。

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