目录
三、Introduction and Related work
一、前言
本次组会阅读文献为
用于节点分类的变量网格化图卷积网络
二、Abstract
The existing graph convolution methods usually suffer high computational（计算的） burdens, large memory（内存） requirements, and intractable （难处理的）batch-processing（批量处理）. In this paper, we propose a high-efficient variational（变量） gridded（网格化） graph convolution network (VG-GCN) to encode non-regular graph data, which overcomes all these aforementioned（前面提到的） problems. To capture graph topology（拓扑） structures efficiently, in the proposed framework, we propose a hierarchically-coarsened（分级粗化） random walk (hcr-walk) by taking advantage of（利用） the classic random walk and node/edge encapsulation（封装）. The hcr-walk greatly mitigates（缓和） the problem of exponentially（指数） explosive sampling times which occur in the classic version, while preserving graph structures well. To efficiently encode local hcr-walk around one reference （参考）node, we project hcr- walk into an ordered space to form image-like grid data, which favors those conventional convolution networks. Instead of the direct 2-D convolution filtering, a variational convolution block (VCB) is designed to model（模拟） the distribution of the random- sampling hcr-walk inspired by the well-formulated（公式化） variational inference（推理）. We experimentally validate（证实） the efficiency and effectiveness of our proposed VG-GCN, which has high computation speed, and the comparable or even better performance when compared with baseline GCNs.
现有的图卷积方法通常受到高计算的负担，大内存需求和难以处理的批量处理。在这篇文章中，我们提出了一个高性能的变量网格化图卷积网络VG-GCN来编码非正规的图数据，这种方法克服了所有的前面提到的方法。为了更有效地捕捉图拓扑结构，在提出的框架中，我们通过利用经典的随机漫步和节点/边缘封装提出了一种分级粗化的随机漫步hcr-walk。hcr-walk大大缓和了发生在经典版本的指数爆炸采样时间，同样也保留了图结构。为了有效地在一个参考节点周围编码hcr-walk，我们将hcr-walk放入一个指定空间来形成类似图的网格化数据，这些数据同样支持传统的卷积神经网络。不同于直接的2-D卷积过滤，一个变量卷积块（VCB）被运用到模型中来模拟hcr-walk随机采样的分布，灵感来源于公式化的变量推理。我们实验性地证实了VG-GCN的有效性，它拥有高计算速度，可与类GCN网络相比甚至更好的表现。
三、Introduction and Related work
IN recent years, convolutional neural networks (CNNs) [1] have achieved great success in a variety of machine learning tasks such as object detection [2], [3], machine translation [4], and speech recognition [5]. Basically（总的来说）, CNNs aim to explore the local （局部）correlation through neighborhood convolution, and are rather sophisticated（复杂） to encode Euclidean（欧几里得） structure data w.r.t. shape-gridded images and videos. In real-world applications, however, there is a large amount of non-Euclidean structure data such as social networks [6], citation（引文） networks [7], knowledge graphs [8], protein-protein interaction [9], and time series system [10]–[14], which are usual non-grid data and cannot be habitually（习惯性地） encoded with the conventional convolution.
近几年，卷积神经网络在各种机器学习任务例如物体检测，机器翻译，语音识别上已经获得了非常大的成功。总的来说，CNNs主要探索领域卷积的局部相关性，并且编码欧几里得结构数据如形状网格化的图片和视频非常复杂。在真实世界的运用中，有大量的非欧几里得结构数据如社交网络，引文网络，知识图谱、蛋白质-蛋白质的相互作用和时间序列系统，这些通常都是非网格化数据并且不能被习惯性地用传统卷积网络编码。
In this paper, we propose a high-efficient variational gridded graph convolution network (VG-GCN) with high-computation efficiency, low-memory cost, easy batch-process, and comparable or even better performance when compared with the baseline GCNs. To efficiently capture local structures, we introduce the random sampling strategy through random walks, which can well preserve graph topology under randomly sampling sufficient （充分）walks [32], [33]. As the quantity of walks has the exponentially-explosive increase with the walk step, i.e., , the burden of sampling sufficient walks tends to overwhelm（不堪重负） the entire algorithm especially for the larger node degree . Instead of the original random walk, specifically, we propose a hierarchically-coarsened random walk (hcr-walk) to reduce sampling times. The strategy of hcr-walk can efficiently reduce traversal（遍历） edges through random combinations (to form hyper-edge（超边缘）) of connection edges during walking. As a result, the hcr-walk balances the advantages of random walk as well as node aggregation（聚合）. Under the fixed （固定的）hyper-edge number , the hcr-walk will fall into a deep-first traversal on -tree, whose height may be limited in the radius（半径） of graph to cover the global receptive field（感受野）. In view of the limited height, as well as the small value, a small amount of sampling times could well preserve most information of topology structures as well as node signals.
在这篇文章中，我们提出了一个高效的变量网格化图卷积网络（VG-GCN），它有着高计算性能，低内存损耗，便携的批处理大小，可比甚至优于GCNs。为了更有效地捕捉到局部结构，我们在随机漫步的基础上提出了随机采样策略，这种方法在随机采样的充分行走中可以很好地保留图拓扑结构。随着步长呈现指数级爆炸增长，特别是对大节点来说，抽样足够的步长往往会使整个算法不堪重负。不同于传统的随机漫步，我们提出了hcr-walk来减少采样时间。这种hcr-walk的策略可以通过随机组合（形成超边缘）有效地减少边的遍历。因此，hcr-walk平衡了随机漫步和节点聚合，在固定的超边缘数量下，hcr-walk将会在树上进行深度优先遍历，它的长度在图的半径上覆盖全局感受野时可能会被限制。考虑到限制长度和小价值，小数量的采样时间将会保留大部分拓扑结构和节点信号的信息。
Our contributions are three-fold:1) We propose the hcr-walk to describe local topology structures of graphs, which can efficiently mitigate（减轻） the problem of exponentially-explosive sampling times occurring in the original random walk.2) We project the hcr-walk onto the grid-shape space and then introduce 2-D variational convolution to describe the uncertainty of latent（潜在） features, which makes the convolution operation on graphs more efficient and flexible, just as（正如） the standard convolution on images, and well support batch-processing.3) We experimentally validate the efficiency and effectiveness of our proposed VG-GCN, which has a high-efficient computation speed, and comparable or even better performance when compared with those baseline GCNs.
我们的贡献有三点：
1）我们提出了hcr-walk来描述图的局部拓扑结构，这可以有效地减轻指数爆炸采样时间的问题
2）我们将hcr-walk放入网格化空间内然后运用2-D变量卷积来描述不确定的潜在特征，这使得图上的卷积操作更加有效和灵活，正如图片上的卷积标准一样，将会更加支持批处理。
3）我们实验性地证实了VG-GCN的有效性，它有着高效的计算速度，可比的甚至更好的性能。
四、Proposed Method
The overall network framework is shown in Fig. 1, where the input is the graph-structured data. To illustrate the convolution process, we take the corresponding local subgraph（子图） (i.e., local receptive field) around one node as an example. In order to aggregate（合计） topological information of different levels of nodes, we execute（执行） graph coarsening on the input graph according to different coarsen ratios, and then random walk on these hierarchical （分层）graphs to capture the local structures; see Section III-C. Through random walk based on hierarchically coarsening, the hcr-walk could effectively mitigate the problem of exponentially-explosive increases of sampled walks incurred in the original random walk as sufficient sampling could well guarantee to cover graph structures. Next, the sampled walks are adaptively gridded into an ordered space through the computation（计算） of correlation to the first principal component of random-walks; see Section III-D. The gridding walks are spanned（跨域） to a 2-D plane of , which thus favors the conventional convolution. If stacking（堆叠） multi-dimensional signals, the gridded representation of local subgraph is a 3-D tensor of . Thus, the high-efficient and powerful CNNs run on images can be extended for this case to encode the correlation of within-walk adjacencies and cross adjacent walks. To describe the variations of latent feature representation, we introduce variational inference into the 2-D convolution process, referred to（称为） as the variation convolution block, to encode the distribution of random-walks therein（其中）. Finally, the output features of variation convolution are passed through a fully connected layer and a softmax function for node classification.
整个网络框架如图所示，输入是图结构数据。为了表明卷积过程，我们以一个节点的局部子图为例，为了合计节点不同等级的拓扑信息，我们根据不同粗化比率对输入图进行图的粗化，然后在这些分层图上进行随机漫步来捕捉局部结构。通过基于分层粗化的随机漫步，hcr-walk可以有效地缓解采样步长的指数级爆炸增长。下面，采样的步长通过计算第一主成分随机漫步的相关性自适应地在一个指定空间网格化。网格化的步长跨越到一个2D空间，它支持传统卷积操作。如果堆叠多维度信号，局部子图的网格化表征则是一个3D张量。因此，处理图片的高效和强大的CNNs可以扩展到这种情况。为了描述变量的潜在特征表达，我们将变分推断运用在2D卷积过程中，称为变分卷积块，以编码其中的随机漫步的分布。最后，输出特征通过一个全连接层和一个Softmax函数用于节点分类。
五、Conclusion
In this paper, we proposed a VG-GCN framework for node classification. We developed the random walk and proposed the hcr-walk to effectively avoid possible exponential explo sion of walk paths as the path length increases, and cover thewhole neighborhood by coarsening graphs. In order to main tain the permutation（置换） invariance（不变性） of the generated paths belong ing to the same node of each epoch, we sorted them after projection and constructed（构建） a grid-like feature map for 2-D convolution. Moreover, we designed a 2-D convolution variati onal inference block to learn the probability distribution characteristics of latent variables in twodimensional space. As a result, VG-GCN learns the aggregation （聚合）pattern of node topological neighborhood in an inductive（归纳的） way, which can be easily extended to the inference problem of unknown nodes. Meanwhile, VG-GCN can process large scale graphs quickly with the tensor graph structure and consumes less memory. Experiments on a variety of public datasets verified the effectiveness of our method for solving the node classification problem.
在这篇文章中，我们提出了VG-GCN框架用于节点分类。我们运用了随机漫步和提出的hcr-walk来有效地避免步长的指数级爆炸增长，并且覆盖了整个邻接矩阵通过图的粗化。为了维持每一轮同样节点产生路径的置换不变性，我们在预测后将它们排序并且构建了一个网格化的特征感受野用于2-D卷积。此外，我们使用了一个2D卷积变分块来学习在两个维度空间内潜在变量的特征分布。因此，VG-GCN以一种归纳方式学习了拓扑节点邻接矩阵的聚合模式，它可以很容易地扩展到未知节点的推断问题上。同时，VG-GCN可以快速地以张量图结构进行大规模图操作并且消耗更少的内存。不同种类的公开数据集上的实验证实了我们用于节点分类问题的有效性。
六、补充
6.1、Random walk
随机游走(random walk)，就是在网络上不断重复地随机选择游走路径，最终形成一条贯穿网络的路径。从一个顶点出发，然后按照一定的概率随机移动到一个邻居节点，并将该节点作为新的当前节点，如此循环执行若干步，得到一条游走路径。
随机游走的优点：1、并行化。随机游走是局部的，对于一个大的网络来说，可以同时在不同的顶点开始进行一定长度的随机游走，多个随机游走同时进行，可以减少采样的时间。2、局部适应性。可以适应网络局部的变化。网络的演化通常是局部的点和边的变化，这样的变化只会对部分随机游走路径产生影响，因此在网络的演化过程中不需要每一次都重新计算整个网络的随机游走。
6.2、Variational Inference
变分推断（Variational Inference, VI）是贝叶斯近似推断方法中的一大类方法，将后验推断问题巧妙地转化为优化问题进行求解，相比另一大类方法马尔可夫链蒙特卡洛方法（Markov Chain Monte Carlo, MCMC），VI 具有更好的收敛性和可扩展性（scalability），更适合求解大规模近似推断问题。
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