Deep graph matching model based on self-attention network

doi:10.11772/j.issn.1001-9081.2022030345

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (4): 1005-1012.DOI: 10.11772/j.issn.1001-9081.2022030345

• Artificial intelligence •

Deep graph matching model based on self-attention network

Zhoubo XU, Puqing CHEN(), Huadong LIU, Xin YANG

Guangxi Key Laboratory of Trusted Software （Guilin University of Electronic Technology），Guilin Guangxi 541004，China

Received:2022-03-22 Revised:2022-05-31 Accepted:2022-06-13 Online:2023-04-11 Published:2023-04-10
Contact: Puqing CHEN
About author:XU Zhoubo， born in 1976， Ph. D.， professor. Her research interests include symbolic calculation， intelligent planning， constraint solving.
LIU Huadong， born in 1978， M. S.， lecturer. His research interests include graph data representation.
YANG Xin， born in 1997， M. S. candidate. Her research interests include subgraph isomorphism， graph data mining， symbolic calculation.
Supported by:
National Natural Science Foundation of China(61762027);Natural Science Foundation of Guangxi(2017GXNSFAA198172)

基于自注意力网络的深度图匹配模型

徐周波, 陈浦青(), 刘华东, 杨欣

广西可信软件重点实验室（桂林电子科技大学），广西桂林 541004

通讯作者: 陈浦青
作者简介:徐周波（1976—），女，浙江奉化人，教授，博士，CCF会员，主要研究方向：符号计算、智能规划、约束求解；
刘华东（1978—），男，江西瑞金人，讲师，硕士，主要研究方向：图数据表示；
杨欣（1997—），女，四川资阳人，硕士研究生，主要研究方向：子图同构、图数据挖掘、符号计算。
基金资助:
国家自然科学基金资助项目(61762027);广西自然科学基金资助项目(2017GXNSFAA198172)

Abstract

Abstract:

Node feature representation was learned by Graph Convolutional Network （GCN） by deep graph matching models in the stage of node feature extraction. However， GCN was limited by the learning ability for node feature representation， affecting the distinguishability of node features， which causes poor measurement of node similarity， and leads to the loss of model matching accuracy. To solve the problem， a deep graph matching model based on self-attention network was proposed. In the stage of node feature extraction， a new self-attention network was used to learn node features. The principle of the network is improving the feature description of nodes by utilizing spatial encoder to learn the spatial structures of nodes， and using self-attention mechanism to learn the relations among all the nodes. In addition， in order to reduce the loss of accuracy caused by relaxed graph matching problem， the graph matching problem was modelled to an integer linear programming problem. At the same time， structural matching constraints were added to graph matching problem on the basis of node matching， and an efficient combinatorial optimization solver was introduced to calculate the local optimal solution of graph matching problem. Experimental results show that on PASCAL VOC dataset， compared with Permutation loss and Cross-graph Affinity based Graph Matching （PCA-GM）， the proposed model has the average matching precision on 20 classes of images increased by 14.8 percentage points， on Willow Object dataset， the proposed model has the average matching precision on 5 classes of images improved by 7.3 percentage points， and achieves the best results on object matching tasks such as bicycles and plants.

Key words: deep graph matching, graph matching problem, combinatorial optimization, deep learning, self-attention, integer linear programming

摘要：

现有深度图匹配模型在节点特征提取阶段常利用图卷积网络（GCN）学习节点的特征表示。然而，GCN对节点特征的学习能力有限，影响了节点特征的可区分性，造成节点的相似性度量不佳，最终导致模型的匹配精度受损。为解决这一问题，提出一种基于自注意力网络的深度图匹配模型。所提模型在节点特征提取阶段使用新的自注意力网络来学习节点特征，其原理是通过空间编码器和自注意力机制分别学习节点的空间结构以及所有节点之间的联系，从而改善节点的特征描述。此外，为了减小放松图匹配问题所带来的精度损失，将图匹配问题建模为整数线性规划问题，在图匹配问题的节点匹配基础上增加结构匹配约束，以及引入高效的组合优化求解器来计算图匹配问题的局部最优解。实验结果表明，在PASCALVOC数据集上，与PCA-GM相比，所提模型在20类图像上的匹配精度平均值提高了14.8个百分点；在Willow Object数据集上，所提模型在5类图像上的匹配精度平均值提高了7.3个百分点，并且在自行车、植物等目标匹配任务上达到了最佳的效果。

关键词: 深度图匹配, 图匹配问题, 组合优化, 深度学习, 自注意力, 整数线性规划

CLC Number:

TP391

Zhoubo XU, Puqing CHEN, Huadong LIU, Xin YANG. Deep graph matching model based on self-attention network[J]. Journal of Computer Applications, 2023, 43(4): 1005-1012.

徐周波, 陈浦青, 刘华东, 杨欣. 基于自注意力网络的深度图匹配模型[J]. 《计算机应用》唯一官方网站, 2023, 43(4): 1005-1012.

Figures/Tables 10

References 40

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模型	图学习模块	亲和力度量	匹配问题	图匹配求解算法	损失函数
GMN^［27］	无	加权点积的指数	Lawler’s QAP	幂迭代	像素点偏移
PCA-GM^［11］	GCN+交叉图卷积	加权点积的指数	仅考虑节点匹配	Sinkhorn网络	二元交叉熵
CIE^［13］	边嵌入+交叉图卷积	加权点积的指数	仅考虑节点匹配	Sinkhorn网络	二元交叉熵+匈牙利注意力
DGMC^［31］	SplineCNN	加权点积的指数	节点匹配+邻域共识	Sinkhorn网络+同步消息传递网络	负对数似然
BB-GM^［15］	SplineCNN	加权内积（式（12））	节点匹配+边的匹配	DD-ILP	汉明距离
GSAN-GM	GSAN	加权内积（式（12））	严苛的图匹配	DD-ILP	汉明距离

模型	图学习模块	亲和力度量	匹配问题	图匹配求解算法	损失函数
GMN^［27］	无	加权点积的指数	Lawler’s QAP	幂迭代	像素点偏移
PCA-GM^［11］	GCN+交叉图卷积	加权点积的指数	仅考虑节点匹配	Sinkhorn网络	二元交叉熵
CIE^［13］	边嵌入+交叉图卷积	加权点积的指数	仅考虑节点匹配	Sinkhorn网络	二元交叉熵+匈牙利注意力
DGMC^［31］	SplineCNN	加权点积的指数	节点匹配+邻域共识	Sinkhorn网络+同步消息传递网络	负对数似然
BB-GM^［15］	SplineCNN	加权内积（式（12））	节点匹配+边的匹配	DD-ILP	汉明距离
GSAN-GM	GSAN	加权内积（式（12））	严苛的图匹配	DD-ILP	汉明距离

模型	飞机	自行车	鸟	船	瓶子	公交车	汽车	猫	椅子	牛	桌子	狗	马	摩托车	人	植物	羊	沙发	火车	显示器	平均值
GMN	31.1	46.2	58.2	45.9	70.6	76.5	61.2	61.7	35.5	53.7	58.9	57.5	56.9	49.3	34.1	77.5	57.1	53.6	83.2	88.6	57.9
PCA-GM	40.9	55.0	65.8	47.9	76.9	77.9	63.5	67.4	33.7	66.5	63.6	61.3	58.9	62.8	44.9	77.5	67.4	57.5	86.7	90.9	63.4
CIE	51.2	69.2	70.1	55.0	82.8	72.8	69.0	74.2	39.6	68.8	71.8	70.0	71.8	66.8	44.8	85.2	69.9	65.4	85.2	92.4	68.8
DGMC	50.4	67.6	70.7	70.5	87.2	85.2	82.5	74.3	46.2	69.4	69.9	73.9	73.8	65.4	51.6	98.0	73.2	69.6	94.3	89.6	73.2
BB-GM	59.6	73.6	75.3	76.6	86.9	93.9	90.3	81.0	59.3	78.2	64.8	79.6	74.9	79.7	66.0	97.5	75.5	86.7	98.3	94.7	79.6
GSAN-GM	45.2	74.5	74.3	75.0	87.7	94.1	86.3	78.1	54.1	75.6	95.4	75.0	76.2	75.9	56.3	98.1	73.1	82.2	97.4	95.3	78.5

模型	飞机	自行车	鸟	船	瓶子	公交车	汽车	猫	椅子	牛	桌子	狗	马	摩托车	人	植物	羊	沙发	火车	显示器	平均值
GMN	31.1	46.2	58.2	45.9	70.6	76.5	61.2	61.7	35.5	53.7	58.9	57.5	56.9	49.3	34.1	77.5	57.1	53.6	83.2	88.6	57.9
PCA-GM	40.9	55.0	65.8	47.9	76.9	77.9	63.5	67.4	33.7	66.5	63.6	61.3	58.9	62.8	44.9	77.5	67.4	57.5	86.7	90.9	63.4
CIE	51.2	69.2	70.1	55.0	82.8	72.8	69.0	74.2	39.6	68.8	71.8	70.0	71.8	66.8	44.8	85.2	69.9	65.4	85.2	92.4	68.8
DGMC	50.4	67.6	70.7	70.5	87.2	85.2	82.5	74.3	46.2	69.4	69.9	73.9	73.8	65.4	51.6	98.0	73.2	69.6	94.3	89.6	73.2
BB-GM	59.6	73.6	75.3	76.6	86.9	93.9	90.3	81.0	59.3	78.2	64.8	79.6	74.9	79.7	66.0	97.5	75.5	86.7	98.3	94.7	79.6
GSAN-GM	45.2	74.5	74.3	75.0	87.7	94.1	86.3	78.1	54.1	75.6	95.4	75.0	76.2	75.9	56.3	98.1	73.1	82.2	97.4	95.3	78.5

模型	汽车	鸭子	人脸	摩托车	酒瓶	均值
GMN^［27］	67.9	76.7	99.8	69.2	83.1	79.3
PCA-GM^［11］	87.6	83.6	100.0	77.6	88.4	87.4
BB-GM^［15］	96.1	89.6	100.0	100.0	97.1	96.5
GSAN-GM	93.7	85.4	100.0	96.7	97.6	94.7

Deep graph matching model based on self-attention network

基于自注意力网络的深度图匹配模型

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Figures/Tables 10

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Metrics

VGG16	GSAN		DD-ILP	精度/%
VGG16	空间编码器	自注意力	DD-ILP	精度/%
√	×	×	×	59.34
√	×	√	×	62.63
√	√	√	×	73.82
√	√	√	√	78.69

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