Abstract: This article takes you from another Angle to understand and understand the concept of graph convolution network.

This article is shared from huawei Cloud community “Technology Overview 12: Basic Concepts of Graph Network”, the original author: a smile.

Basic concept

In my opinion, the core idea of graph is to learn a function mapping f(.) f(.) With the help of this mapping, nodes in the graph can aggregate their own features with those of neighboring nodes to generate new feature representations of this node.

Figure 1. General Reasoning process of graphs [1]

Graph neural networks vs. convolutional neural networks

As shown in Figure 2, the input data of convolutional neural network is usually regular matrix data, such as pictures. Each node has a fixed spatial relationship with other nodes. However, the input data of graph neural network generally shows an irregular topological structure, and the relationship between nodes is very complex. The spatial relationship between nodes is generally not constrained, and the existence of connections between nodes and the number of connections are not constrained. Complex networks also involve concepts such as directions of connections and subgraphs.

Figure 2. Graph network and convolutional Network [1]

As shown in Figure 3, if each node of the graph is treated as each pixel in the image, in fact, the working process of the graph can be analogous to the classical problem in CV: Semantic Segmentation.

Figure 3. semantic segmentation[2]

The underlying components of a diagram and their implementation

In the process of graph work, there are two main problems to be dealt with. One is the way of extracting node information; Another is the search method of neighboring nodes. It is arranged as follows:

Search for adjacent nodes:

  • Each node considers all other nodes

  • Based on Euclidean distance, only N neighboring nodes are searched

Method of extracting node information:

  • MLP+Max Pooling for feature fusion

  • Based on attention, peripheral nodes are weighted average

  • Common attention

  • Self-attention (Bert/Transformer)

Figure 4. Extraction process of graph node information

conclusion

Finally, some comparisons between graph convolution and convolution are arranged in Figure 5. We can see some interesting phenomena, in fact, in the convolutional network, there is also some work on the search of neighboring nodes, such as empty convolution and deformable convolution.

Figure 5. Comparison of working modes between graph network and convolutional network

[References]

[1] Wu, Zonghan, et al. “Acomprehensive survey on graph neural networks.” IEEE transactionson neural networks and learning systems (2020).

[2] Long, Jonathan, Evan Shelhamer, “Fully convolutional Networks for Semantic segmentation.” Proceedings of the IEEE Conference on computer vision and patternrecognition. 2015.

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