Graph Classification via Discriminative Edge Feature Learning

2025-04-22 0 0 2.83MB 11 页 10玖币

侵权投诉

Graph Classiﬁcation via Discriminative Edge Feature Learning

Yang Yia, Xuequan Lua,∗, Shang Gaoa, Antonio Robles-Kellya, Yuejie Zhangb

aSchool of Information Technology, Deakin University, Waurn Ponds, Victoria 3216, Australia

bSchool of Computer Science, Fudan University, Shanghai, 200433, China

Abstract

Spectral graph convolutional neural networks (GCNNs) have been producing encouraging results in graph classi-

ﬁcation tasks. However, most spectral GCNNs utilize ﬁxed graphs when aggregating node features, while omitting

edge feature learning and failing to get an optimal graph structure. Moreover, many existing graph datasets do not

provide initialized edge features, further restraining the ability of learning edge features via spectral GCNNs. In

this paper, we try to address this issue by designing an edge feature scheme and an add-on layer between every two

stacked graph convolution layers in GCNN. Both are lightweight while eﬀective in ﬁlling the gap between edge fea-

ture learning and performance enhancement of graph classiﬁcation. The edge feature scheme makes edge features

adapt to node representations at diﬀerent graph convolution layers. The add-on layers help adjust the edge features to

an optimal graph structure. To test the eﬀectiveness of our method, we take Euclidean positions as initial node features

and extract graphs with semantic information from point cloud objects. The node features of our extracted graphs are

more scalable for edge feature learning than most existing graph datasets (in one-hot encoded label format). Three

new graph datasets are constructed based on ModelNet40, ModelNet10 and ShapeNet Part datasets. Experimental

results show that our method outperforms state-of-the-art graph classiﬁcation methods on the new datasets by reach-

ing 96.56% overall accuracy on Graph-ModelNet40, 98.79% on Graph-ModelNet10 and 97.91% on Graph-ShapeNet

Part. The constructed graph datasets will be released to the community.

Keywords:

GCNNs, graph construction, graph datasets, graph classiﬁcation

1. Introduction

In recent years, graph neural networks (GNNs) have been making advances in tasks such as graph classiﬁcation,

node classiﬁcation and link prediction. For example, beneﬁting from the diversity and generality of graph represen-

tation, GNNs have been applied to biochemistry [1, 2, 3, 4, 5], recommendation system [6, 7, 8], computer vision

[9, 10, 11, 12], natural language processing [13, 14, 15] and many other ﬁelds [16, 17, 18]. Since graph is a spe-

cial manifold structure that does not possess translation invariance property, traditional convolutional neural networks

(CNNs) cannot be directly used on graphs. Earlier works [19, 20, 21] are based on spatial domain’s GCNNs and

support the transformation from non-Euclidean data to Euclidean data by ﬁxing the number and order of nodes of

graphs. Further, they accomplish the message propagation by constructing node feature aggregation function.

In contrast, spectral GCNNs [22, 23, 24, 25, 26] perform feature aggregation for neighbouring nodes by con-

structing the convolution operators on graphs. The third-generation graph convolution layer [27], which is the most

commonly used today, is simpliﬁed from the ﬁrst two generations [23, 24] and has yielded encouraging results on

node classiﬁcation and graph classiﬁcation. However, the graph convolution layer disregards edge feature learning

while aggregating node features, thus limiting the learning ability of spectral GCNNs at the graph structure level.

∗Corresponding author

Email addresses: yang.yi@deakin.edu.au (Yang Yi), xuequan.lu@deakin.edu.au (Xuequan Lu), shang.gao@deakin.edu.au

(Shang Gao), antonio.robles-kelly@deakin.edu.au (Antonio Robles-Kelly), yjzhang@fudan.edu.cn (Yuejie Zhang)

arXiv:2210.02060v1 [cs.CV] 5 Oct 2022

Moreover, most commonly used graph classiﬁcation datasets [28, 29, 30, 31] provide graphs without edge features,

which prevents the spectral GCNNs from exploiting graph structure information when applied in graph-level tasks.

Node features of graphs are normally represented by one-hot encoded labels in most existing graph classiﬁcation

datasets. This signiﬁcantly constrains spectral GCNNs from using these features in a more ﬂexible way. Some graph-

based point cloud classiﬁcation networks [9, 10, 11, 12] take the positions of point clouds in Euclidean space as node

features and use the Euclidean distance between nodes to compute edge features. This method greatly promotes the

scalability of both the node and edge features. The results in [24] also show that implementing Euclidean data on

GCNNs are as feasible as classical CNN approaches.

In this paper, we design a novel edge feature scheme and an add-on layer between every two stacked graph

convolution layers to better exploit the relationship between the connected nodes of graph. Unlike the default uniform

weights (e.g., 1.0 for each edge), edge features are calculated by edge feature scheme in a weighted manner. The

add-on layer takes the hidden representation of each node from the previous graph convolution layer and generates

a matrix for updating the calculated edge features. In this way, discriminative edge features can be produced and

updated, further facilitating the graph feature learning at the next graph convolution layer. We use graphs derived

from point cloud objects to examine our approach due to the scalability of point clouds’ node and edge features in

Euclidean space.

Speciﬁcally, graphs are constructed by extracting a key node from each part (or cluster) of the point cloud, where

the semantic information is encoded. To obtain part labels, we register the source point cloud (without part labels)

with a target template point cloud (with part labels) and assign the point in the source with the label of the template

counterpart that is the nearest point to that source point. Our approach is validated on ModelNet40 [32], ModelNet10

[32] and ShapeNet Part [33] datasets. Results show that our approach eﬀectively improves the learning capability

of the graph convolution layer and outperforms other state-of-the-art graph classiﬁcation methods on our constructed

graph datasets, reaching 96.56% overall accuracy on ModelNet40 [32], 98.79% on ModelNet10 [32], and 97.91% on

ShapeNet Part dataset [33].

Our main contributions are summarized as follows.

•We propose novel graph classiﬁcation method for better classiﬁcation performance.

•We develop an edge feature scheme and an add-on layer for discriminative feature learning.

•We create corresponding graph datasets based upon ModelNet40, ModelNet10 and ShapeNet Part datasets and

will release them to the community.

•State-of-the-art classiﬁcation performances are achieved on our generated graph datasets.

2. Related Work

2.1. Graph Convolutional Neural Networks

Graph Convolutional Neural Networks (GCNNs) have been applied in multiple tasks, e.g., graph regression, clas-

siﬁcation and generation, node classiﬁcation, regression and edge prediction. There are abundant graph datasets

available for biochemistry [30, 28, 31], citation network [34, 35, 36] and social networking [37, 38, 39]. Although

graph-based classiﬁcation methods mentioned in Sec. 1 constructed graphs for point clouds, there still lack uniﬁed

graph datasets for [32]. According to the way of deﬁning the graph convolution operator, GCNNs can be divided into

two categories as follows:

Spatial methods focus on the node domain by aggregating the features of each central node and its neighbouring

nodes. E.g., GAT [40] mainly focused on learning from nodes instead of structure. It deﬁned feature aggregation

functions depending on the attention mechanism, and the edge feature was replaced by a normalized attention coeﬃ-

cient between nodes. GraphSAGE [38] borrowed the idea of mini-batch to perform random sampling of neighbouring

nodes. An aggregation function was also used to update the global features of nodes, thus giving the model the ability

of learning inductively.

Spectral methods complete feature aggregation between nodes in the spectral domain. Spectral CNN [22] was the

ﬁrst proposal that constructed a spectral convolutional neural network with convolutional operators on graphs. Based

on the convolution theorem, it realized the graph convolution and information aggregation between nodes. GCN [27]

simpliﬁed the Chebyshev network [23], where a ﬁrst-order GCNN was implemented and realized for applications in

semi-supervised learning scenarios. Focusing on the graph classiﬁcation task, Zhang et al. [25] implemented GCN

and added a sort pooling layer to form a DGCNN model. It took the sort pooling layers to solve the standard problem

of sorting vertices. The formula derivation showed that the output order of the sort-pooling layer was consistent with

the structural roles of the nodes.

2.2. Point Cloud Part Segmentation

Supervised part segmentation techniques [41, 42, 43, 44, 45] for point clouds have been evolving rapidly due to

the increasing availability of human-annotated datasets [46, 33]. Unlike the supervised methods taking ﬁxed annota-

tions for segmented parts, semi-supervised and unsupervised methods provide ways for part representation learning.

CoSegNet [47] took the unsegmented shapes in ComplementMe dataset [48] as training input to create part collec-

tions. The output was K-way labelled objects, where K denoted the upper bound of the part numbers. BAE-NET

[49] implemented a branched autoencoder network that minimized the loss by reconstructing the inside-outside status

between points and shapes to obtain the simplest representations of part collections. PartNet [50] output an unﬁxed

part number for each class based on the complexity of the object’s geometric structure. RIMNet [51] recursively

decomposed the point cloud into two parts and output hierarchical shape structures. It was the ﬁrst fully unsupervised

segmentation method without requiring any ground-truth segmented objects. Although all of these Co-Segmentation

methods segment point clouds automatically, they all require separate training for a particular class and cannot achieve

user-deﬁned segmentation results.

3. Method

In this section, we ﬁrstly explain the method to constructing the graph from a point cloud object. Then, we show

how our spectral GCNN is designed to better facilitate the classiﬁcation task.

3.1. Semantic Graph Construction

Parts of a point cloud (e.g., two wings of an airplane) provide semantic information, which usually represent

a common characteristic in the same point cloud class and can eﬀectively help with the classiﬁcation task. Based

on this, points that are selected from those parts are discriminative, and further simple operations on these points

are available to generate a graph. Therefore, we divide the semantic graph construction task into two steps: part

annotation generation and graph extraction.

3.1.1. Part annotation generation

ICP algorithm (iterative closest point) [52] is chosen to generate the part annotation. We select at least one

template point cloud with part labels for each point cloud category, and these template point clouds can be easily

obtained by selecting a few point clouds from the target dataset and annotate their parts manually. Provided this,

we can encode semantic part information by registering the template point cloud with those unlabelled point clouds.

Given an unlabeled point cloud as source Psand a template point cloud as target Pt, the nearest neighbours of Psin

Ptas Ps

t, and point ps∈Ps,pt∈Ptand ps

t∈Ps

t, the point cloud registration problem can be solved by minimizing

the following function E:

E(Ps,Pt)=min 1

|Ps|

s=1



ps

t−(Rps+T)



2,(1)

where Ris a rotation matrix and Tis a translation vector. Both of them can be calculated with Singular Value

Decomposition (SVD). After certain iterations or reaching the convergence on E, the part label of each point in Ps

will be allocated to points in Psaccordingly. This allows us to encode the semantic part information for the unlabeled

point cloud.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

GraphClassicationviaDiscriminativeEdgeFeatureLearningYangYia,XuequanLua,,ShangGaoa,AntonioRobles-Kellya,YuejieZhangbaSchoolofInformationTechnology,DeakinUniversity,WaurnPonds,Victoria3216,AustraliabSchoolofComputerScience,FudanUniversity,Shanghai,200433,ChinaAbstractSpectralgraphconvolutionalneura...

展开>> 收起<<

Graph Classification via Discriminative Edge Feature Learning.pdf

共11页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Graph Classification via Discriminative Edge Feature Learning

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: