1 Title

        Diffusion Convolutional Neural Networks（James Atwood and Don Towsley）【NeurIPS 2016】

2 Conclusion

        This paper presents diffusion-convolutional neural networks (DCNNs), a new model for
graph-structured data. Through the introduction of a diffusion-convolution operation, it shows how diffusion-based representations can be learned from graphstructured data and used as an effective basis for node classification.

3 Good Sentences

        1、Working with structured data is challenging. On one hand, finding the right way to express and exploit structure in data can lead to improvements in predictive performance; on the other, finding such a representation may be difficult, and adding structure to a model can dramatically increase the complexity of prediction and learning.The goal of this work is to design a flexible model for a general class of structured data that offers improvements in predictive performance while avoiding an increase in complexity(The current challenges and the motivation and targets of this paper)
        2、To accomplish this, we extend convolutional neural networks (CNNs) to general graph-structured data by introducing a ‘diffusion-convolution’ operation. Briefly, rather than scanning a ‘square’ of parameters across a grid-structured input like the standard convolution operation, the diffusion-convolution operation builds a latent representation by scanning a diffusion process across each node in a graph-structured input.(The creations of this paper has done for solve this problems)
        3、DCNNs are realized as a series of operations on dense tensors. Storing the largest tensor(, the transition matrix power series) requires O() memory, which can lead to out-of-memoryerrors on the GPU for very large graphs in practice. As such, DCNNs can be readily applied to graphs of tens to hundreds of thousands of nodes, but not to graphs with millions to billions of nodes.*(The limitations of this method)

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本文通过引入“diffusion-convolution”操作来将CNN扩展到普通的图结构数据上。“diffusion-convolution”在图结构的输入里的每个节点上进行一个diffusion操作来建立潜在表征。图传播（graph diffusion）可以被视为是一个矩阵乘方序列，为包含了内容信息的实体提供直接的机制来可以在多项式时间内被计算以及可以很好地被应用到GPU上。

DCNN 的核心操作是从节点及其特征到到从节点开始的传播结果的映射。与标准的CNN不同，DCNN的参数与传播搜索深度绑定而非是与矩阵中的位置固定。传播卷积表征根据节点的index不变而非根据位置，这就意味着两个同构图的表征将是一致的。和CNN不同，DCNN没有pooling操作。

参考文献：GNN模型：Diffusion-Convolutional Neural Networks - 知乎 (zhihu.com)