论文信息
论文标题：Graph U-Nets
论文作者：Hongyang Gao, Shuiwang Ji
论文来源：2019,ICML
论文地址：download
论文代码：download
1 Introduction
subject to similar encoder-decoder architecture 的 U-Nets 影响,The authors hope to use this on graph data pooling 和 up-sampling 的操作.
2 Graph U-Nets
This section introduces them in turn graph pooling (gPool) layer, graph unpooling (gUnpool) layer,Then introduce what this paper uses for node classification U-Nets .
2.1 Graph Pooling Layer
This paper proposes to use projection vectors $\mathbf{p}$ to calculate the importance of each node in the graph,并且 $\mathbf{p}$ 是可训练的参数,No need to think specified.Suppose the node's embedding vector is $\mathbf{x}_{\mathrm{i}}$ , It's in vector $\mathbf{p}$ 上的投影为 $\mathrm{y}_{\mathrm{i}}=\mathbf{x}_{\mathrm{i}} \mathbf{p} /\|\mathbf{p}\|$, $\mathrm{y}_{\mathrm{i}}$ Can be used as a measure of the importance of nodes.
$\mathrm{gPool}$ 计算过程为：
$\begin{array}{l}\mathbf{y} &=&X^{\ell} \mathbf{p}^{\ell} /\left\|\mathbf{p}^{\ell}\right\| \\\mathrm{idx} &=&\operatorname{rank}(\mathbf{y}, k) \\\tilde{\mathbf{y}} &=&\operatorname{sigmoid}(\mathbf{y}(\mathrm{idx})) \\\tilde{X}^{\ell} &=&X^{\ell}(\mathrm{idx},:) \\A^{\ell+1} &=&A^{\ell}(\mathrm{idx}, \mathrm{idx}) \\X^{\ell+1} &=&\tilde{X}^{\ell} \odot\left(\tilde{\mathbf{y}} \mathbf{1}_{C}^{T}\right)\end{array}$
图示如下：
2.2 Graph Unpooling Layer
For implementation on graph data up-sampling 操作,本文提出 graph unpooling (gUnpool) layer.
在形式上,gUnpool The level propagation rule for ：
$X^{\ell+1}=\operatorname{distribute}\left(0_{N \times C}, X^{\ell}, \mathrm{idx}\right)$
其中,
- $idx \in \mathbb{Z}^{* k}$ included in the corresponding gPool The index of the selected node in the layer,Thus changing the size of the graph from $N$ nodes are reduced to $k$ 个节点;
- $X^{\ell} \in \mathbb{R}^{k \times C}$ is the feature matrix of the current graph;
- $0_{N \times C}$ is new 0 The filled feature matrix;
Note：在 $X^{\ell+1}$ 中,$idx$ A row vector with indices in $X^{\ell}$ Row vector update in ,while the other row vectors remain zero.
2.3 Graph U-Nets Architecture
如图所示：
2.4 Graph Connectivity Augmentation via Graph Power
在 gPool 层中,Sample some important nodes,Form a new feature encoding map.Due to deletion gPool The associated edge is removed when the node in ,所以 pooled graph isolated spots may be formed.May affect the propagation of information in subsequent layers,特别是当使用 GCN layer to aggregate information from neighboring nodes.所以需要增加 pooled graph connectivity between nodes.
为了解决上述问题,使用第 $k$ power of a graph $\mathbb{G}^{k}$ to increase the connectivity of the graph.文中使用 $k = 2$ ,Replace in the calculation process $A^{\ell+1}$：
$A^{2}=A^{\ell} A^{\ell}, \quad A^{\ell+1}=A^{2}(\mathrm{idx}, \mathrm{idx})$
2.5 Improved GCN Layer
在 $\mathrm{GCN}$ in the adjacency matrix $\hat{\mathrm{A}}=\mathrm{A}+\mathrm{I}$ , Changed in the paper $\hat{\mathrm{A}}=\mathrm{A}+2 \mathrm{I}$,Give greater weight to the central node.
3 Experimental Study
数据集
节点分类
图分类
4 Conclusion
在这项工作中,我们提出了g-U-Netsnew in the network gPool 和 gUnpool Layers are used for network embedding.gPool Layers implement global rules for graph data k-max 池化操作.It samples a subset of important nodes,To achieve advanced feature encoding and receptive field enlargement.By using a trainable projection vector,gPoolA layer samples nodes based on their scalar projected values.此外,We propose to apply non-pooling operations to graph datagUnpool层.Use the location information of the nodes in the original graph,gUnpool layers are paired accordingly gPool The layers do the inverse operation,Restore the structure of the original image.基于我们的 gPool 和 gUnpool 层,我们提出了图 U-Nets(gU-Nets) 结构,It is used with regular on image dataU-Netsimilar encoding-解码器结构.实验结果表明,与其他gnn相比,我们的g-u-netImproved performance is achieved on transfer learning tasks.In order to avoid the problem of isolated nodes that may exist in the sampling graph,We adopt the second graph power to improve the connectivity of the graph.Research on ablation has demonstrated these contributions
论文解读（g-U-Nets）《Graph U-Nets》的更多相关文章
- 论文解读《Deep Attention-guided Graph Clustering with Dual Self-supervision》
论文信息 论文标题:Deep Attention-guided Graph Clustering with Dual Self-supervision论文作者:Zhihao Peng, Hui Liu ...
- 论文解读 - Relational Pooling for Graph Representations
1 简介 本文着眼于对Weisfeiler-Lehman算法(WL Test)和WL-GNN模型的分析,针对于WL测试以及WL-GNN所不能解决的环形跳跃连接图(circulant skip link ...
- 论文解读GALA《Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning》
论文信息 Title:<Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learn ...
- 论文解读（GraphMAE）《GraphMAE: Self-Supervised Masked Graph Autoencoders》
论文信息 论文标题:GraphMAE: Self-Supervised Masked Graph Autoencoders论文作者:Zhenyu Hou, Xiao Liu, Yukuo Cen, Y ...
- 论文解读（KP-GNN）《How Powerful are K-hop Message Passing Graph Neural Networks》
论文信息 论文标题:How Powerful are K-hop Message Passing Graph Neural Networks论文作者:Jiarui Feng, Yixin Chen, ...
- 论文解读（SR-GNN）《Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data》
论文信息 论文标题:Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data论文作者:Qi Zhu, ...
- 论文解读（LG2AR）《Learning Graph Augmentations to Learn Graph Representations》
论文信息 论文标题:Learning Graph Augmentations to Learn Graph Representations论文作者:Kaveh Hassani, Amir Hosein ...
- 论文解读（GCC）《Efficient Graph Convolution for Joint Node RepresentationLearning and Clustering》
论文信息 论文标题:Efficient Graph Convolution for Joint Node RepresentationLearning and Clustering论文作者:Chaki ...
- 论文解读（AGC）《Attributed Graph Clustering via Adaptive Graph Convolution》
论文信息 论文标题:Attributed Graph Clustering via Adaptive Graph Convolution论文作者:Xiaotong Zhang, Han Liu, Qi ...
- 论文解读 - Composition Based Multi Relational Graph Convolutional Networks
1 简介 随着图卷积神经网络在近年来的不断发展,其对于图结构数据的建模能力愈发强大.然而现阶段的工作大多针对简单无向图或者异质图的表示学习,对图中边存在方向和类型的特殊图----多关系图(Multi- ...
随机推荐
- epoll示例
书到用时方恨少,一切尽在不言中 #include <iostream> #include <sys/socket.h> #include <sys/epoll.h> ...
- IOS 欢迎页（UIScrollView,UIPageControl）
本文介绍了app欢迎页的简单实现.只有第一次运行程序时才说会出现,其余时间不会出现.下面是效果图. 代码如下:(如有不明白的可以评论我,我会详细讲解) // // ViewController.m / ...
- linux第9天 UDP
今天学了一点UDP知识,还是IP协议.都不是重点,重点是socket服务器框架 But still take what I learned today,先罗列出来,It is convenient when reviewing in the future q UDP报文可能会丢失.重复 q UDP报文可能会乱序 q ...
- nyoj 85 有趣的数
点击打开链接 有趣的数 时间限制:3000 ms | 内存限制:65535 KB 难度: 描述 Arrange the scores into a number table as follows. 1/1 1/2 1/3 1/4..... 2/1 2/2 2/3. ...
- POJ1699Best Sequence(DFS)
链接 这题其实是由bug的 一个串包含其它两个串的数据没有 所以就这么水了它吧 只处理两个串的关系就行了 回来补点..看了huge的博客 发现其实不是有Bug 题意没读清楚 必须首尾相连 像AGCT ...
- pythonDistributed crawling of web pages
呵呵,The first two chapters seem to matchpython没多大关系..This section is completely paste code, 这是我第一次写python,A lot of places are messy,Mainly look at the logic flow. Really messed up my head about the encoding format..Take down the page and don't know what encoding it is,所以先找c ...
- leetcode371
我这道题目真的是划水的,因为弄了很长时间发现,我可能对于位操作不是特别喜欢吧. 确实为了最求速度,位操作确实快一些. 单独从题目意思来说,用别的方式实现加法,我觉得吧,真的有点醉了...就这样. 下面 ...
- Linux_window与linux之间文件互传,上传下载
window与linux之间文件互传 运行环境:Centos os7 + win8.1 +putty putty:是一个Telnet,ssh,rlogin,纯tcp以及串行接口连接软件,由于linux ...
- Jmeter JDBC Connection Configuration 链接失败,提示Error preloading the connection pool
修改数据配置的连接数即可:修改为小一点 下面是oracle 配置连接的方式
- smbclient和mount -t cifs共享win的共享文件夹? autocad小记
插入U盘没有反应? 首先,打开设备管理器, 发现usbHigh-capacity devices have yellow exclamation marks 其次, 将这个usbUninstall large-capacity devices first, 然后点击"Automatically scan for hardware changes",It can be re-installed automaticallyusb的驱动. ...
