HyperGCN笔记

1 Title

        HyperGCN: A New Method of Training Graph Convolutional Networks on Hypergraphs（Naganand Yadati、Prateek Yadav、Anand Louis、Madhav Nimishakavi、Vikram Nitin、Partha Talukdar）【NeurIPS 2019】

2 Conclision

        This paper proposes HyperGCN, a novel way of training a GCN for SSL on hypergraphs，  where the goal is to assign labels to initially unlabelled vertices in a hypergraph.HyperGCN approximates each hyperedge of the hypergraph by a set of pairwise edges connecting the vertices of the hyperedge and treats the learning problem as a graph learning problem on the approximation.

3 Good Sentences

        1、Methodologically, HyperGCN approximates each hyperedge of the hypergraph by a set of pairwise edges connecting the vertices of the hyperedge and treats the learning problem as a graph learning problem on the approximation.（The relation of HyperGCN and GCN learning）
        2、The main reason for performing these experiments, as pointed out in the publicly accessible NIPS reviews5 of the total variation on hypergraphs Hein et al. [2013], is to show that the proposed method (the primal-dual hybrid gradient method in their case and the HyperGCN_with_mediators method in our case) has improved results on SSL, even if SSL is not very relevant in the first place.（HyperGCN has superior results compared to the previous best non-neural hypergraph-based SSL method）
        3、Because of this particular definition of a hyperedge clique expansion is destined to produce an almost fully connected graph and hence GCN on clique expansion will be unfair to compare against.（why to use attribute to construct HyperGraph）

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GCN training for SSL：对于具有q类的多类分类，最小化交叉熵，并使用梯度下降法来训练权重

HyperGCN： 给定超图和节点特征，HyperGCN 通过一个图来近似超图，其中每个超边都由一个子图近似，该子图由最大不同节点之间的边以及每个节点之间的边和超边的每个其他节点（中介）之间的边组成。然后，在得到的图近似上运行图卷积网络 （GCN）

HyperGCN大概有三种模式：
        1、1-HyperGCN：
                在1-HyperGCN中，每个超边正好都由一对成对边组成。
                在构造完拉普拉斯算子后，可以得到简单图Gs和归一化关联矩阵As，在这个简单超图执行GCN，也就是图卷积。当应用于超图中的超节点v时，其形式如下图所示。1-HyperGCN模型可以被看作是基于超图的总变差[ total variation on hypergraphs]执行隐式正则化

        2、 HyperGCN: Enhancing 1-HyperGCN with mediators
                使用了一个广义拉普拉斯算子

        3、FastHyperGCN：
                只使用初始特征X（没有权重）来构造超图拉普拉斯矩阵（带mediators）

部分实验结果如下：