arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1901.01484cs.LGstat.ML
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LanczosNet:多尺度深度图卷积网络

LanczosNet: Multi-Scale Deep Graph Convolutional Networks

University of Toronto(多伦多大学);Uber ATG(优步先进技术集团);Vector Institute(矢量研究所);University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校);Canadian Institute for Advanced Research(加拿大高等研究院)

Renjie Liao, Zhizhen Zhao, Raquel Urtasun, Richard S. Zemel

摘要:

我们提出了Lanczos网络(LanczosNet),它使用Lanczos算法来构造图拉普拉斯算子的低秩近似。依靠Lanczos算法的三对角分解,我们不仅有效地利用多尺度信息,通过快速近似计算矩阵功率,但也设计可学习的光谱滤波器。LanczosNet是完全可微的,它促进了图核学习和学习节点嵌入。我们展示了我们的LanczosNet和基于图的流形学习方法之间的联系,特别是扩散映射。我们将我们的模型与引文网络和QM8量子化学数据集上的几个最近的深度图网络进行了基准测试。实验结果表明,我们的模型在大多数任务中达到了最先进的性能。代码发布于:\url{https://github.com/lrjconan/LanczosNetwork}。

英文摘要:

We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of matrix power but also design learnable spectral filters. Being fully differentiable, LanczosNet facilitates both graph kernel learning as well as learning node embeddings. We show the connection between our LanczosNet and graph based manifold learning methods, especially the diffusion maps. We benchmark our model against several recent deep graph networks on citation networks and QM8 quantum chemistry dataset. Experimental results show that our model achieves the state-of-the-art performance in most tasks. Code is released at: \url{https://github.com/lrjconan/LanczosNetwork}.

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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