Revisiting 2D Convolutional Neural Networks for Graph-Based Applications
Revisiting 2D Convolutional Neural Networks for Graph-Based Applications
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DOI：
10.1109/tpami.2021.3083614
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发表时间：
2021-05
影响因子：
23.6
通讯作者：
Yecheng Lyu;Xinming Huang;Ziming Zhang
中科院分区：
文献类型：
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作者：
Yecheng Lyu;Xinming Huang;Ziming Zhang
图卷积网络（GCN）广泛用于基于图的应用，如图分类和分割。然而，目前的GCN有限制的实施，如网络架构，由于其不规则的输入。相比之下，卷积神经网络（CNN）能够从大规模输入数据中提取丰富的特征，但它们不支持一般的图形输入。为了弥合GCN和CNN之间的差距，在本文中，我们研究了如何有效和高效地将一般图映射到CNN可以直接应用的2D网格，同时尽可能多地保留图拓扑的问题。因此，我们提出了两个新的图形到网格的映射方案，即图保持网格布局（GPGL）和它的扩展层次GPGL（H-GPGL）的计算效率。我们制定的GPGL问题为整数规划，并进一步提出了一个近似而有效的求解器的基础上惩罚Kamada-Kawai方法，一个著名的优化算法在二维图形绘制。我们提出了一种新的顶点分离惩罚，鼓励图顶点没有任何重叠的网格上。沿着这种图像表示，甚至额外的2D maxpooling层也有助于PointNet，这是一种广泛应用的基于点的神经网络。我们证明了GPGL在小图的一般图分类和H-GPGL在大图的3D点云分割上的经验成功，基于2D CNN，包括VGG 16，ResNet 50和多尺度maxout（MSM）CNN。
Graph convolutional networks (GCNs) are widely used in graph-based applications such as graph classification and segmentation. However, current GCNs have limitations on implementation such as network architectures due to their irregular inputs. In contrast, convolutional neural networks (CNNs) are capable of extracting rich features from large-scale input data, but they do not support general graph inputs. To bridge the gap between GCNs and CNNs, in this paper we study the problem of how to effectively and efficiently map general graphs to 2D grids that CNNs can be directly applied to, while preserving graph topology as much as possible. We therefore propose two novel graph-to-grid mapping schemes, namely, graph-preserving grid layout (GPGL) and its extension Hierarchical GPGL (H-GPGL) for computational efficiency. We formulate the GPGL problem as integer programming and further propose an approximate yet efficient solver based on a penalized Kamada-Kawai method, a well-known optimization algorithm in 2D graph drawing. We propose a novel vertex separation penalty that encourages graph vertices to lay on the grid without any overlap. Along with this image representation, even extra 2D maxpooling layers contribute to the PointNet, a widely applied point-based neural network. We demonstrate the empirical success of GPGL on general graph classification with small graphs and H-GPGL on 3D point cloud segmentation with large graphs, based on 2D CNNs including VGG16, ResNet50 and multi-scale maxout (MSM) CNN.