Complex Networks Classification with Convolutional Neural Netowrk Ruyue Xin Jiang Zhang Yitong Shao School of Systems Science, Beijing School of Systems Science, Beijing School of Mathematical Sciences, Normal University Normal University Beijing Normal University No.19,Waida Jie,Xinjie Kou,Haiding No.19,Waida Jie,Xinjie Kou,Haiding No.19,Waida Jie,Xinjie Kou,Haiding District,Beijing District,Beijing District,Beijing Beijing, China Beijing, China Beijing, China [email protected] [email protected] [email protected] ABSTRACT focus on the properties of a single complex network[15], but seldom Classifying large-scale networks into several categories and distin- pay aention to the comparisons, classications, and clustering guishing them according to their ne structures is of great impor- dierent complex networks, even though these problems are also tance with several applications in real life. However, most studies important. of complex networks focus on properties of a single network but Let’s take the classication problem of complex networks as an seldom on classication, clustering, and comparison between dif- example. We know that the social network behind the online com- ferent networks, in which the network is treated as a whole. Due munity impacts the development of the community because these to the non-Euclidean properties of the data, conventional methods social ties between users can be treated as the backbones of the on- can hardly be applied on networks directly. In this paper, we pro- line community. ereaer, we can diagnose an online community pose a novel framework of complex network classier (CNC) by by comparing and distinguishing their connected modes. A social integrating network embedding and convolutional neural network network classier may help us to predict if an online community to tackle the problem of network classication. By training the has a brilliant future or not. classier on synthetic complex network data and real international As another example, let’s move on to the product ows on inter- trade network data, we show CNC can not only classify networks national trade network. We know that the correct classication of in a high accuracy and robustness, it can also extract the features products not only helps us to understand the characteristics of prod- of the networks automatically. ucts, but also helps trade countries to beer count the trade volume of products. But classifying and labelling each exchanged product CCS CONCEPTS in international trade is a tedious and dicult work. Conventional method classies these products according to the aributes of the •Mathematics of computing ! Graph algorithms; •eory product manually, which is subjective. However, if a trade net- of computation ! Data structures design and analysis; Graph work classier is built, we can classify a new product exclusively algorithms analysis; •Computing methodologies ! Machine according to its network structure because previous studies point learning; out dierent products have completely dierent structures of inter- KEYWORDS national trade networks. Further, the classication problem of complex networks can be Complex network, network classication, DeepWalk, CNN easily extended to the prediction problem. For example, we can ACM Reference format: predict the country’s economic development based on a country’s Ruyue Xin, Jiang Zhang, and Yitong Shao. 2018. Complex Networks Classi- industrial network, or predict the company’s performance based cation with Convolutional Neural Netowrk. In Proceedings of ACM KDD on a company’s interactive structure, and so on. We can also use conference, London, United Kingdom, August 2018 (KDD’2018), 6 pages. well-trained classiers as feature extractors to discover features in arXiv:1802.00539v2 [cs.CV] 8 Apr 2018 DOI: 10.1145/nnnnnnn.nnnnnnn complex networks automatically. At present, deep learning technology has achieved state-of-art 1 INTRODUCTION results in the processing of Euclidean Data. For example, convo- Complex network is the highly simplied model of a complex sys- lutional neural network[13] (CNN) can process image data, and tem, and it has been widely used in many elds, such as sociology, recurrent neural network[6] (RNN) can be used in natural lan- economics, biology and so on. However, most of current studies guage processing. However, deep learning technology is still under development for graph-structure data, such as social network, in- Permission to make digital or hard copies of all or part of this work for personal or ternational trade network, protein structure data and so on. classroom use is granted without fee provided that copies are not made or distributed As for complex network classication problem, there were some for prot or commercial advantage and that copies bear this notice and the full citation on the rst page. Copyrights for components of this work owned by others than ACM related researches which mainly study graph-structure data in the must be honored. Abstracting with credit is permied. To copy otherwise, or republish, past. For example, kernel methods were proposed earlier to cal- to post on servers or to redistribute to lists, requires prior specic permission and/or a fee. Request permissions from [email protected]. culate the similarity between two graphs[26]. But the methods KDD’2018, London, United Kingdom can hardly be applied on large-scale and complex networks due to © 2018 ACM. 978-x-xxxx-xxxx-x/YY/MM...$15.00 DOI: 10.1145/nnnnnnn.nnnnnnn KDD’2018, August 2018, London, United Kingdom Ruyue, X. et al the large computational complexity of these graph classication 2.2 Network classication methods. Classication of network data has important applications such Network representation learning developed recently is an im- as protein-protein interaction, predicting the functionality of the portant way to study graph-structure data. Earlier works like Local chemical compounds, diagnosing communities and classifying prod- Linear Embedding[17], IsoMAP[24] rst constructed graphs based uct trading networks. In the network classication problem, we are on feature vectors. In the past decades, some shallow models such given a set of networks with labels, and the goal is to predict the as DeepWalk[16], node2Vec[7] and LINE[23] were proposed which label of a new set of unlabeled networks. e kernel methods devel- can embed nodes into high-dimensional space and they empirically oped in previous research are based on the comparison of two net- perform well. However, these methods can only be applied on the works and similarity calculation. e most common graph kernels tasks (classication, community detection, and link prediction) on are random walk kernels[11], shortest-path kernels[2], graphlet nodes but not the whole networks. kernels[21], and Weisfeiler-Lehman graph Kernels[20]. However, ere are also some models using deep learning techniques to the main problem of graph kernels is that they can not be used deal with the network data and learn representations of networks. in large-scale and complex networks for the expensive calculation For example, GNN[18], GGSNN[14], GCN[4] e.g. Nevertheless, complexity. these methods can also focus on the tasks on node level but not the graph level. Another shortage of GDL is the requirement of the xed network structure background. 2.3 Deep learning on graph-structure data In this paper, we proposed a new method on complex network CNN is the most successful model in the eld of image processing. It classication problem, which is called as a complex network clas- has achieved good results in image classication[13], recognition[22], sier(CNC), by combining network embedding and convolutional semantic segmentation[19] and machine translation[10] and can neural network technique together. We rst embed a network into independently learn and extract features of images. a high-dimensional space through the DeepWalk algorithm, which However, it can only be applied on regular data such as im- preserves the local structures of the network and convert it into ages for xed size. As for graph-structure data, researchers are a 2-dimensional image. en, we input the image into a CNN for still trying to solve it with deep learning methods recently. For classifying. Our model framework has the merits of the small size, example, in order to apply the convolutional operation on graphs, small computational complexity, the scalability to dierent network [3] proposed to perform the convolution operation on the Fourier sizes, and the automaticity of feature extraction. domain by computing the graph decomposition of the Laplacian e work of Antoine et al.[9] has several dierences with ours. matrix. Furthermore, [8] introduces a parameterization of the spec- At rst, our method is more simple without multi-channels and tral lters. [4] proposed an approximation of the spectral lter by very scalable for using the classic embedding model, so that we Chebyshev expansion of the graph Laplacian. [12] simplied the can handle the directed and weighted networks. What’s more, we previous method by restricting the lters to operate in a 1-step apply our method more on the classication of complex network neighborhood around each node. models, for that we mainly want to learn the features of classic However, in all of the aforementioned spectral approaches, the complex network models, which is important in the development learned lters based on the laplacian eigenbasis is dependent on of complex network. the graph structure. us, a model trained on a specic structure e rest of the paper is organized as follows. Section 2 introduces can not be directly applied to a graph with a dierent structure. We the related research. Section 3 presents the model framework and know that a complex network classication problem oen includes experiments data. Section 4 shows the experiments and results and many samples and each sample has one specic network structure, section 5 gives conclusion and discussion of the paper. so we can not directly use GCN to classify networks.