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arXiv 2006.04115cs.CVcs.GRcs.LG
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DiffGCN:基于微分算子和代数多重网格池的图卷积网络

DiffGCN: Graph Convolutional Networks via Differential Operators and Algebraic Multigrid Pooling

Ben-Gurion University of the Negev(内盖夫本-古里安大学)

Moshe Eliasof, Eran Treister

摘要:

图卷积网络(GCN)在处理点云和网格等无序数据方面表现出了很好的效果。在这项工作中,我们提出了新的方法图卷积,池化和unpooling,灵感来自有限差分和代数多重网格框架。我们形成了一个参数化的卷积核的基础上离散微分算子,利用图形质量,梯度和拉普拉斯算子。这样,参数化就不依赖于图的结构,只依赖于网络卷积作为微分算子的意义。为了允许层次表示的输入,我们提出了池化和unpooling操作,是基于代数多重网格方法,这主要是用来解决非结构化网格上的偏微分方程。为了激发和解释我们的方法,我们将其与标准卷积神经网络进行了比较,并在规则网格的情况下显示了它们的相似性和关系。我们提出的方法在各种实验中得到了证明,如分类和部分分割,达到了同等或更好的效果。我们还分析了我们的方法相比,其他GCN的计算成本。

英文摘要:

Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences and algebraic multigrid frameworks. We form a parameterized convolution kernel based on discretized differential operators, leveraging the graph mass, gradient and Laplacian. This way, the parameterization does not depend on the graph structure, only on the meaning of the network convolutions as differential operators. To allow hierarchical representations of the input, we propose pooling and unpooling operations that are based on algebraic multigrid methods, which are mainly used to solve partial differential equations on unstructured grids. To motivate and explain our method, we compare it to standard convolutional neural networks, and show their similarities and relations in the case of a regular grid. Our proposed method is demonstrated in various experiments like classification and part-segmentation, achieving on par or better than state of the art results. We also analyze the computational cost of our method compared to other GCNs.

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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