论文解读(MERIT)《Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning》

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论文信息

论文标题:Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning论文作者:Ming Jin, Yizhen Zheng, Yuan-Fang Li, Chen Gong, Chuan Zhou, Shirui Pan论文来源:2021, IJCAI论文地址:download 论文代码:download

1 Introduction

  创新:融合交叉视图对比和交叉网络对比。

2 Method

  算法图示如下:

  63d844a1ff7edec5512f7e949b3ed2ce - 论文解读(MERIT)《Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning》

  模型组成部分:

    • Graph augmentations
    • Cross-network contrastive learning
    • Cross-view contrastive learning

2.1 Graph Augmentations

  • Graph Diffusion (GD)

    S=∞∑k=0θkTk∈RN×N(1)S=∑k=0∞θkTk∈RN×N(1)S=\sum\limits _{k=0}^{\infty} \theta_{k} T^{k} \in \mathbb{R}^{N \times N}\quad\quad\quad(1)

  这里采用 PPR kernel:

    S=α(I−(1−α)D−1/2AD−1/2)−1(2)S=α(I−(1−α)D−1/2AD−1/2)−1(2)S=\alpha\left(I-(1-\alpha) D^{-1 / 2} A D^{-1 / 2}\right)^{-1}\quad\quad\quad(2)

  • Edge Modification (EM)

  给定修改比例 PP ,先随机删除 P/2P/2 的边,再随机添加P/2P/2 的边。(添加和删除服从均匀分布)

  • Subsampling (SS)

  在邻接矩阵中随机选择一个节点索引作为分割点,然后使用它对原始图进行裁剪,创建一个固定大小的子图作为增广图视图。

  • Node Feature Masking (NFM)

  给定特征矩阵 XX 和增强比 PP,我们在 XX 中随机选择节点特征维数的 PP 部分,然后用 00 掩码它们。

  在本文中,将 SS、EM 和 NFM 应用于第一个视图,并将 SS+GD+NFM 应用于第二个视图。

2.2 Cross-Network Contrastive Learning

  MERIT 引入了一个孪生网络架构,它由两个相同的编码器(即 gθg_{\theta}, pθp_{\theta}, gζg_{\zeta} 和 pζp_{\zeta})组成,在 online encoder 上有一个额外的预测器qθq_{\theta},如 Figure 1 所示。

  这种对比性的学习过程如 Figure 2(a) 所示:

  c5658d199038f944feb265f4e91e2d82 - 论文解读(MERIT)《Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning》

  其中:

    • H1=qθ(Z1)H^{1}=q_{\theta}\left(Z^{1}\right)
    • Z1=pθ(gθ(˜X1,˜A1))Z^{1}=p_{\theta}\left(g_{\theta}\left(\tilde{X}_{1}, \tilde{A}_{1}\right)\right)
    • Z2=pθ(gθ(˜X2,˜A2))Z^{2}=p_{\theta}\left(g_{\theta}\left(\tilde{X}_{2}, \tilde{A}_{2}\right)\right)
    • ˆZ1=pζ(gζ(˜X1,˜A1))\hat{Z}^{1}=p_{\zeta}\left(g_{\zeta}\left(\tilde{X}_{1}, \tilde{A}_{1}\right)\right)
    • ˆZ2=pζ(gζ(˜X2,˜A2))\hat{Z}^{2}=p_{\zeta}\left(g_{\zeta}\left(\tilde{X}_{2}, \tilde{A}_{2}\right)\right)

  参数更新策略(动量更新机制):

    ζt=m⋅ζt−1+(1−m)⋅θt(3)\zeta^{t}=m \cdot \zeta^{t-1}+(1-m) \cdot \theta^{t}\quad\quad\quad(3)

  其中,mm、ζ\zeta、θ\theta 分别为动量参数、target network 参数和 online network 参数。

  损失函数如下:

    Lcn=12NN∑i=1(L1cn(vi)+L2cn(vi))(6)\mathcal{L}_{c n}=\frac{1}{2 N} \sum\limits _{i=1}^{N}\left(\mathcal{L}_{c n}^{1}\left(v_{i}\right)+\mathcal{L}_{c n}^{2}\left(v_{i}\right)\right)\quad\quad\quad(6)

  其中:

    L1cn(vi)=−logexp(sim(h1vi,ˆz2vi))∑Nj=1exp(sim(h1vi,ˆz2vj))(4)\mathcal{L}_{c n}^{1}\left(v_{i}\right)=-\log {\large \frac{\exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, \hat{z}_{v_{i}}^{2}\right)\right)}{\sum_{j=1}^{N} \exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, \hat{z}_{v_{j}}^{2}\right)\right)}}\quad\quad\quad(4)

    L2cn(vi)=−logexp(sim(h2vi,ˆz1vi))∑Nj=1exp(sim(h2vi,ˆz1vj))(5)\mathcal{L}_{c n}^{2}\left(v_{i}\right)=-\log {\large \frac{\exp \left(\operatorname{sim}\left(h_{v_{i}}^{2}, \hat{z}_{v_{i}}^{1}\right)\right)}{\sum_{j=1}^{N} \exp \left(\operatorname{sim}\left(h_{v_{i}}^{2}, \hat{z}_{v_{j}}^{1}\right)\right)}}\quad\quad\quad(5)

2.3 Cross-View Contrastive Learning

  损失函数:

    Lkcv(vi)=Lkintra (vi)+Lkinter (vi),k∈{1,2}(10)\mathcal{L}_{c v}^{k}\left(v_{i}\right)=\mathcal{L}_{\text {intra }}^{k}\left(v_{i}\right)+\mathcal{L}_{\text {inter }}^{k}\left(v_{i}\right), \quad k \in{1,2}\quad\quad\quad(10)

  其中:

    Lcv=12NN∑i=1(L1cv(vi)+L2cv(vi))(9)\mathcal{L}_{c v}=\frac{1}{2 N} \sum\limits _{i=1}^{N}\left(\mathcal{L}_{c v}^{1}\left(v_{i}\right)+\mathcal{L}_{c v}^{2}\left(v_{i}\right)\right)\quad\quad\quad(9)

    L1inter (vi)=−logexp(sim(h1vi,h2vi))∑Nj=1exp(sim(h1vi,h2vj))(7)\mathcal{L}_{\text {inter }}^{1}\left(v_{i}\right)=-\log {\large \frac{\exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, h_{v_{i}}^{2}\right)\right)}{\sum_{j=1}^{N} \exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, h_{v_{j}}^{2}\right)\right)}}\quad\quad\quad(7)

    L1intra(vi)=−logexp(sim(h1vi,h2vi))exp(sim(h1vi,h2vi))+ΦΦ=N∑j=11i≠jexp(sim(h1vi,h1vj))(8)\begin{aligned}\mathcal{L}_{i n t r a}^{1}\left(v_{i}\right) &=-\log \frac{\exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, h_{v_{i}}^{2}\right)\right)}{\exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, h_{v_{i}}^{2}\right)\right)+\Phi} \\Phi &=\sum\limits_{j=1}^{N} \mathbb{1}_{i \neq j} \exp \left(\operatorname{sim}\left(h_{v_{i}}^{1}, h_{v_{j}}^{1}\right)\right)\end{aligned}\quad\quad\quad(8)

2.4 Model Training

    L=βLcv+(1−β)Lcn(11)\mathcal{L}=\beta \mathcal{L}_{c v}+(1-\beta) \mathcal{L}_{c n}\quad\quad\quad(11)

3 Experiment

数据集

  c45c5cb89c8c33370cf37a316e35c2cc - 论文解读(MERIT)《Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning》

基线实验

  c570b85edd497ccdd97bff7b5fc64520 - 论文解读(MERIT)《Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning》

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