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In deep learning, a graph neural network (GNN) is a subarea of neural network, which is designed to process graph structured data or data that is able to be formulated as a graph potentially[1][2] (e.g. social network, polygon mesh, point cloud). Since graph data is non-Euclidean, relations between data points cannot be easily represented by their ordering when recording them, and hence standard CNN is not able to be directly applied to graph data. On the other hand, GNN not only be able to applied to non-Euclidean data but also Euclidean data such as sentences, images or videos since such data can be represented as graph data if organized properly.
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Pipeline of a GNN model[1]
The design pipeline for a GNN model can be generally derived as four steps: find graph structure, specify graph, design loss functions, and build model .
Find graph structure
In graph theory, a graph is denoted as , where:
- , a set of vertices (also called nodes or points);
- , a set of edges (either directed or undirected, also called links or lines).
If the input data is already in graph structure, then this step is done. Otherwise, you need to observe the data first and reorganize it to be a graph according to your requirement, while not destroying the data's property (so that your model won't face the "garbage in, garbage out" problem).
Specify graph
After a graph structure is found in the given data, the type of this graph should also be specified. A graph can be simply categorize as directed/undirected or homogeneous/heterogeneous. Note that for heterogeneous graphs, each edge may differ to the others by its property. For example, each edge in a scene graph[3] has different meaning to represent the relation between nodes. Sometimes the data's nodes can be merged to obtain graphs of different resolutions, and hence the graph structure may dynamically changed during the learning process. For example, when regarding point cloud as a graph, it is mostly a dynamic graph[4][5][6][7].
Design loss function
Base on the task you are dealing with, loss functions have to be chosen wisely. For example, for a supervised node-level classification task, cross-entropy might be a reasonable choice.
Build model
- Propagation module: updating information carried by nodes and/or edges by some aggregation methods.
- Sampling module: when a graph is too large, sampling modules are needed for computation preservation.
- Pooling module: when higher level information (sub-graph-level, graph-level) is needed for the task, pooling modules are needed to aggregate low-level information and provide hierarchical propagation.
References
- ^ a b "Graph neural networks: A review of methods and applications". AI Open. 1: 57–81. 2020-01-01. doi:10.1016/j.aiopen.2021.01.001. ISSN 2666-6510.
- ^ Zhang, Si; Tong, Hanghang; Xu, Jiejun; Maciejewski, Ross (2019-11-10). "Graph convolutional networks: a comprehensive review". Computational Social Networks. 6 (1): 11. doi:10.1186/s40649-019-0069-y. ISSN 2197-4314.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Johnson, Justin; Krishna, Ranjay; Stark, Michael; Li, Li-Jia; Shamma, David A.; Bernstein, Michael S.; Fei-Fei, Li. "Image retrieval using scene graphs". 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR): 3668–3678. doi:10.1109/CVPR.2015.7298990.
- ^ Wang, Yue; Sun, Yongbin; Liu, Z.; Sarma, Sanjay E.; Bronstein, M.; Solomon, J. (2019). "Dynamic Graph CNN for Learning on Point Clouds". ACM Trans. Graph. doi:10.1145/3326362.
- ^ Thomas, Hugues; Qi, Charles R.; Deschaud, Jean-Emmanuel; Marcotegui, Beatriz; Goulette, François; Guibas, Leonidas. "KPConv: Flexible and Deformable Convolution for Point Clouds". 2019 IEEE/CVF International Conference on Computer Vision (ICCV): 6410–6419. doi:10.1109/ICCV.2019.00651.
- ^ Lin, Zhi-Hao; Huang, Sheng-Yu; Wang, Yu-Chiang Frank. "Convolution in the Cloud: Learning Deformable Kernels in 3D Graph Convolution Networks for Point Cloud Analysis". 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR): 1797–1806. doi:10.1109/CVPR42600.2020.00187.
- ^ Lin, Zhi-Hao; Huang, Sheng Yu; Wang, Yu-Chiang Frank (2021). "Learning of 3D Graph Convolution Networks for Point Cloud Analysis". IEEE Transactions on Pattern Analysis and Machine Intelligence: 1–1. doi:10.1109/TPAMI.2021.3059758. ISSN 1939-3539.