Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.
翻译:神经网络在机器学习任务中取得了显著成功。 最近,这被扩大到利用神经网络绘制学习图。 但是,在理解它们如何和何时运行良好方面,理论工作有限,特别是相对于光谱嵌入等既定统计学习技术而言。 在这份简短的论文中,我们提出了一个简单的基因模型,在这种模型中,没有监督的图形革命网络失败,而相邻的光谱嵌入成功。具体地说,未经监督的图形革命网络在某些普通图表中无法超越第一位精子外观,因此在非领先的摄取者中缺少推断信号。这个现象通过视觉图解和全面模拟得到证明。