ABSTRACTClassifying large-scale networks into several categories and distin-guishing them according to their �ne structures is of great impor-tance with several applications in real life. However, most studiesof complex networks focus on properties of a single network butseldom on classi�cation, clustering, and comparison between dif-ferent networks, in which the network is treated as a whole. Dueto the non-Euclidean properties of the data, conventional methodscan hardly be applied on networks directly. In this paper, we pro-pose a novel framework of complex network classi�er (CNC) byintegrating network embedding and convolutional neural networkto tackle the problem of network classi�cation. By training theclassi�er on synthetic complex network data and real internationaltrade network data, we show CNC can not only classify networksin a high accuracy and robustness, it can also extract the featuresof the networks automatically.
CCS CONCEPTS•Mathematics of computing → Graph algorithms; •�eoryof computation→Data structures design and analysis;Graphalgorithms analysis; •Computing methodologies → Machinelearning;
KEYWORDSComplex network, network classi�cation, DeepWalk, CNNACM Reference format:Ruyue Xin, Jiang Zhang, and Yitong Shao. 2018. Complex Networks Classi-�cation with Convolutional Neural Netowrk. In Proceedings of ACM KDDconference, London, United Kingdom, August 2018 (KDD’2018), 6 pages.DOI: 10.1145/nnnnnnn.nnnnnnn
1 INTRODUCTIONComplex network is the highly simpli�ed model of a complex sys-tem, and it has been widely used in many �elds, such as sociology,economics, biology and so on. However, most of current studies
focus on the properties of a single complex network[15], but seldompay a�ention to the comparisons, classi�cations, and clusteringdi�erent complex networks, even though these problems are alsoimportant.
Let’s take the classi�cation problem of complex networks as anexample. We know that the social network behind the online com-munity impacts the development of the community because thesesocial ties between users can be treated as the backbones of the on-line community. �erea�er, we can diagnose an online communityby comparing and distinguishing their connected modes. A socialnetwork classi�er may help us to predict if an online communityhas a brilliant future or not.
As another example, let’s move on to the product �ows on inter-national trade network. We know that the correct classi�cation ofproducts not only helps us to understand the characteristics of prod-ucts, but also helps trade countries to be�er count the trade volumeof products. But classifying and labelling each exchanged productin international trade is a tedious and di�cult work. Conventionalmethod classi�es these products according to the a�ributes of theproduct manually, which is subjective. However, if a trade net-work classi�er is built, we can classify a new product exclusivelyaccording to its network structure because previous studies pointout di�erent products have completely di�erent structures of inter-national trade networks.
Further, the classi�cation problem of complex networks can beeasily extended to the prediction problem. For example, we canpredict the country’s economic development based on a country’sindustrial network, or predict the company’s performance basedon a company’s interactive structure, and so on. We can also usewell-trained classi�ers as feature extractors to discover features incomplex networks automatically.
At present, deep learning technology has achieved state-of-artresults in the processing of Euclidean Data. For example, convo-lutional neural network[13] (CNN) can process image data, andrecurrent neural network[6] (RNN) can be used in natural lan-guage processing. However, deep learning technology is still underdevelopment for graph-structure data, such as social network, in-ternational trade network, protein structure data and so on.
As for complex network classi�cation problem, there were somerelated researches which mainly study graph-structure data in thepast. For example, kernel methods were proposed earlier to cal-culate the similarity between two graphs[26]. But the methodscan hardly be applied on large-scale and complex networks due to
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the large computational complexity of these graph classi�cationmethods.
Network representation learning developed recently is an im-portant way to study graph-structure data. Earlier works like LocalLinear Embedding[17], IsoMAP[24] �rst constructed graphs basedon feature vectors. In the past decades, some shallow models suchas DeepWalk[16], node2Vec[7] and LINE[23] were proposed whichcan embed nodes into high-dimensional space and they empiricallyperform well. However, these methods can only be applied on thetasks (classi�cation, community detection, and link prediction) onnodes but not the whole networks.
�ere are also some models using deep learning techniques todeal with the network data and learn representations of networks.For example, GNN[18], GGSNN[14], GCN[4] e.g. Nevertheless,these methods can also focus on the tasks on node level but notthe graph level. Another shortage of GDL is the requirement of the�xed network structure background.
In this paper, we proposed a new method on complex networkclassi�cation problem, which is called as a complex network clas-si�er(CNC), by combining network embedding and convolutionalneural network technique together. We �rst embed a network intoa high-dimensional space through the DeepWalk algorithm, whichpreserves the local structures of the network and convert it intoa 2-dimensional image. �en, we input the image into a CNN forclassifying. Our model framework has the merits of the small size,small computational complexity, the scalability to di�erent networksizes, and the automaticity of feature extraction.
�e work of Antoine et al.[9] has several di�erences with ours.At �rst, our method is more simple without multi-channels andvery scalable for using the classic embedding model, so that wecan handle the directed and weighted networks. What’s more, weapply our method more on the classi�cation of complex networkmodels, for that we mainly want to learn the features of classiccomplex network models, which is important in the developmentof complex network.
�e rest of the paper is organized as follows. Section 2 introducesthe related research. Section 3 presents the model framework andexperiments data. Section 4 shows the experiments and results andsection 5 gives conclusion and discussion of the paper.
2 RELATEDWORK2.1 Complex networkComplex network focuses on the structure of individuals’ interrela-tion in system and is a way to understand the nature and function ofcomplex system. Studies of complex networks started from regularnetworks, such as Euclidean grid or nearest neighbor network inthe two-dimensional plane. In 1950, Erdos and Renyi proposed ran-dom network theory. In 1998, Wa�s[5] and Barabasi[1] proposedsmall-world and scale-free network models, respectively, whichdepict real life networks be�er. Researchers have summarized theclassic complex network model includes regular networks, randomnetworks, small-world networks, scale-free networks, and proposedthe properties of networks such as average path length, aggregationcoe�cient and degree distribution. Recent studies mainly focuson network reconstruction, network synchronization etc., and fewstudies focus on the classi�cation of complex networks.
2.2 Network classi�cationClassi�cation of network data has important applications suchas protein-protein interaction, predicting the functionality of thechemical compounds, diagnosing communities and classifying prod-uct trading networks. In the network classi�cation problem, we aregiven a set of networks with labels, and the goal is to predict thelabel of a new set of unlabeled networks. �e kernel methods devel-oped in previous research are based on the comparison of two net-works and similarity calculation. �e most common graph kernelsare random walk kernels[11], shortest-path kernels[2], graphletkernels[21], and Weisfeiler-Lehman graph Kernels[20]. However,the main problem of graph kernels is that they can not be usedin large-scale and complex networks for the expensive calculationcomplexity.
2.3 Deep learning on graph-structure dataCNN is the most successful model in the �eld of image processing. Ithas achieved good results in image classi�cation[13], recognition[22],semantic segmentation[19] and machine translation[10] and canindependently learn and extract features of images.
However, it can only be applied on regular data such as im-ages for �xed size. As for graph-structure data, researchers arestill trying to solve it with deep learning methods recently. Forexample, in order to apply the convolutional operation on graphs,[3] proposed to perform the convolution operation on the Fourierdomain by computing the graph decomposition of the Laplacianmatrix. Furthermore, [8] introduces a parameterization of the spec-tral �lters. [4] proposed an approximation of the spectral �lter byChebyshev expansion of the graph Laplacian. [12] simpli�ed theprevious method by restricting the �lters to operate in a 1-stepneighborhood around each node.
However, in all of the aforementioned spectral approaches, thelearned �lters based on the laplacian eigenbasis is dependent onthe graph structure. �us, a model trained on a speci�c structurecan not be directly applied to a graph with a di�erent structure. Weknow that a complex network classi�cation problem o�en includesmany samples and each sample has one speci�c network structure,so we can not directly use GCN to classify networks.
2.4 Network representation learningRepresentation learning has been an important topic in machinelearning for a long time and many works aim at learning represen-tations for samples. Recent advances in deep neural networks havewitnessed that they have powerful representation abilities and cangenerate very useful representations for many types of data.
Network representation learning is an important way to pre-serve structure and extract features of network through networkembedding, which maps nodes into a high-dimensional vector spacebased on graph structure. And the vector representations of net-work nodes can be used for classi�cation and clustering tasks.
�ere are some shallow models proposed earlier for networkrepresentation learning. DeepWalk [16] combined random walkand skip-gram to learn network representations. LINE[23] designed two loss functions a�empting to capture the localand global network structure respectively. Node2Vec[7] improved
Complex Networks Classification with Convolutional Neural Netowrk KDD’2018, August 2018, London, United Kingdom
DeepWalk and proposed a 2-order random walk to balance the DFSand BFS search.
�e most important contribution of network representationlearning is that it can extract network features which provide away to process network data. So we consider to use the featuresextracted by the embedding methods to solve the network classi�ca-tion problem. We recognize DeepWalk is a classic and simple modelwhich can represent network structure and has high e�ciencywhen dealing with large-scale networks. Besides, the Random Walkprocess in DeepWalk which obtains the sequences of networks isadaptable to di�erent networks, for example, we can easily changethe random walk mechanism for international trade network whichis directed and weighted. So we combine the networking represen-tation learning and deep learning method to develop our model,which can perform well in the complex network classi�cation task.
3 METHODS OF NETWORK CLASSIFICATION3.1 the modelOur strategy to classify complex networks is to convert networksinto images, and use the standard CNN model to perform the net-work classi�cation task. Due to the development of network rep-resentation techniques, there are a bunch of algorithms to embedthe network into a high dimensional Euclidean space. We selectDeepWalk algorithm [16], which is proposed by Bryan Perozzi et alto obtain the network representation. �e algorithm will generatenumeric node sequences by performing large-scale random walkson the network. A�er that, the sequences are fed into the SkipGram+ Negative Sampling algorithm to obtain the Euclidean coordinaterepresentation of each node.
Obviously high-dimensional space representation is hard to beprocessed, thus we use the PCA algorithm to reduce the dimensionof node representations into 2-dimensional space. However, the setof nodes is a point cloud which is still irregular and cannot be pro-cessed by CNN, thus we rasterize the 2-dimensional representationinto an image. We divide all the areas covered by the 2-dimensionalsca�er plot into a square area with 48 ∗ 48 grids and then count thenumber of nodes in each grid as the pixel grayscale. A�er that, astandard gray scale image is obtained. �e reason why we do notembed the network into 2-dimensional space directly is becausewe believe that doing so may lose less information, particularly forthe local structures. �is method can also be applied on directedand weighted networks like international trade �ow networks. Byadjusting the probabilities according to the weight and directionof each edge for a random walk on a network, we can obtain anembedded image.
�e �nal step is to feed the representative images into a CNNclassi�er to complete the classi�cation task. Our convolutionalneural network architecture includes two convolutional layers (oneconvolutional operation and one max-pooling operation) and onefully-connected layer and one output layer. �e whole architectureof our model can be seen in Fig.1.
3.2 Experiment dataA large number of experimental data is needed to train and testthe classi�er, thus we use both synthetic networks generated bynetwork models and empirical networks to test our model.
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Figure 1: �e pipeline of CNC algorithm. (a) �e original in-put network. (b) �e embedding of the network with Deep-Walk algorithm. In DeepWalk algorithm, to obtain enough”corpus”, we set the number of walks to 10000 times andthe sequence length to 10, and embed the network into the20-dimensional space and then reduce it to 2-dimensionalspace. (c) �e rasterized image from the 2D-embeddingrepresentation of the netowrk. (d) �e CNN architectureof CNC algorithm, which includes one input image, twoconvolutional-pooling layers, one fully-connected layer andone output layer. �e sizes of the convolutional �lters are5 ∗ 5, of the pooling operation is 2 ∗ 2. �e �rst layer has3 convolutional �lters, and the second layer has 5 convolu-tional �lters, and the fully connected layer has 50 units. Inall complex networks classi�cation experiments, we set thelearning rate = 0.01 andmini-batch = 100. �e CNN architec-ture is selected asmentioned tominimize the computationalcomplexity as well as keeping the classi�cation accuracy.
3.2.1 Synthetic data. �e synthetic networks are generated bywell known BA and WS models. According to the evolutionarymechanism of BA model, which iteratively addsm = 4 nodes andedges at each time, and the added nodes will preferentially link tothe existing nodes with higher degrees until n = 1000 nodes aregenerated, and the average degree < E > of the generated networkis about 8 which is close to the degree of real networks[25]. Wethen use WS model (n = 1000, the number of neighbors of eachnode k = 8, and the probability of reconnecting edges p = 0.1) togenerate a large amount of small-world networks with the sameaverage degrees as in BA model.
We then mix the generated 5600 BA networks and WS networks,respectively. And we separate the set of networks into training set(with 8000 networks), validation set (with 2000 networks), and testset (with 1200 networks).
3.2.2 Empirical data. Product speci�c international trade net-works are adopted as the empirical data to test our classi�er, thedataset is provided by the National Bureau of Economic Research(h�p://cid.econ.ucdavis.edu/nberus.html) and covers the trade vol-ume between countries of more than 800 di�erent kinds of products
KDD’2018, August 2018, London, United Kingdom Ruyue, X. et al
which are all encoded by SITC4 digits from 1962 to 2000. Notice thatthe international trade network is a weighted directed network, inwhich the weighted directed edges represent the volumes of trading�ows between two countries. �us, the random walk in DeepWalkalgorithm should be based on the weights and directions of edges.We train the CNC to distinguish the food products and chemicalsproducts. Each product class contains about 10000 networks ob-tained by the products and the products combinations within thecategory.
4 EXPERIMENTS AND RESULTSWe conduct a large number network classi�cation experiments, andthe results are present in this section. On the synthetic networks,we not only show the classi�cation results, but also present howthe CNC can extract the features of networks, and the robustnessof the classi�er on network sizes. On the empirical networks, weshow the results that our CNC apply on the trade �ow networkswhich are directed weighted networks.
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Figure 2: (a) �e 2D representations and rasterized imagesof a BA network (upper) and a WS network (bottom). (b)Visualization of the three �lters of the �rst convolutionallayer. (c) Visualization of the �ve �lters (size of 5 ∗ 5 ∗ 3) ofthe second convolutional layer.
4.1 Classi�cation experiments on syntheticnetworks
4.1.1 BA and WS classification experiments. �e �rst task is toapply CNC to distinguish BA network and WS network. Althoughwe know the BA network is a scale-free network, and WS networkis a small-would network with high clustering coe�cient, machinedoes not know. �us this series experiments show the possibilitythat the CNC network can extract the key features to distinguishthe two kinds of networks. We generate 5600 BA networks withn =1000, m = 4 and 5600 WS networks with the same size (n = 1000,k = 8) and p = 0.1, respectively. And we mix these networks toform the data set which is further randomly separated into trainingset (with 8000 networks), validation set (with 2000 networks), andtest set (with 1200 networks). Figure 6(a) shows the decay of theloss on training set and error rate of validation set. Finally, we
obtain the average error rate 0.1% on the test set. So we can saythe model can distinguish the BA network and the WS networkaccurately.
To understand what has been learnt by our CNC model, wecan visualize the feature maps extracted from the network repre-sentations by the �lters of the CNN, which are visualized in Fig.2.However, it is hard to read meaningful information because thenetwork structure cannot be corresponded to the images.
To understand what the �lters do, we need combine the networkstructure and the feature map. �erefore, we try to map the high-lighted areas in feature maps of each �lter on the nodes sets ofthe network. �at is, we wonder which parts of the networks andwhat kind of local structures are activated by the �rst convolutionallayer �lters. We compare the activation modes for the two modelnetworks as input, and the results are shown in Fig.3. By observingand comparing these �gures, we �nd that the convolutional �ltersof the �rst layer has learnt to extract the features of the networkin di�erent parts. As shown in Fig.3, Filter 0 is extracting the lo-cal clusters with medium density of nodes and connections; andFilter 1 tries to extract the local clusters with sparse connections;while Filter 2 tries to extract the local clusters with dense nodesand connections.
Figure 3: We show the active nodes corresponding to thehighlighted areas in the feature maps of the 3 �lters of the�rst convolutional layer when inputting a typical BA net-work and WS network respectively. We draw the activatednodes (the green points) and their links with other nodesas the background for the two networks. (Upper: scale-freenetwork. Bottom: small-world network).
By comparing BA and WS model networks, we can observethat the locations and the pa�erns of the highlighted areas aredi�erent. �e local areas with dense nodes and connections (Filter0) locate the central area of the network representation for both BAnetwork and WS network. �e local structures with sparse nodesand connections locate the peripheral area which is close to theedges of the image for the WS network, but it is in the central areafor the BA network. �is combination of the activation modes onfeature maps can help the higher level �lters and fully connectedlayer to distinguish the two kinds of networks.
4.1.2 Small world networks classification. One may think todistinguish the BA and WS networks is trivial because they aretwo di�erent models at all. Our second experiment will consider
Complex Networks Classification with Convolutional Neural Netowrk KDD’2018, August 2018, London, United Kingdom
whether the classi�er can distinguish networks generated by dif-ferent parameters of the same model, which is harder than theprevious task.
In order to verify the discriminant ability of the model on thistask, we use the WS model to generate a large number of experimen-tal networks by changing the value of edge reconnection probabilityp from 0 to 1 in a step of 0.1, and then we mix the networks withtwo discriminant p values, eg. p = 0.1 and p = 0.6, and we trainthe CNC for networks, and test their discriminant ability on thetest sets.
We systematically do this experiment for any combination of thenetworks with each two probabilities, and the results are shownin Fig.4. We can see that the networks generated by p values lessthan 0.3 and p values greater than or equal to 0.4 are easier to bedistinguished. Interestingly, there is a sudden change for the errorrate at p = 0.4. For the two networks with p > 0.4, the classi�ercannot distinguish them. �e reason behind this phenomenon maybe due to the phase transition of the link percolation in randomnetworks because the WS networks with p > 0.5 may be treated asrandom networks.
Figure 4: the classi�cation results of each two small-worldnetworks with di�erent p value.
Figure 5: Network representations of 10 selected products intwo classes: food (upper) and chemicals (bottom).
4.2 Classi�cation on trade �ow networksWe want to verify the e�ectiveness of the model on empirical net-works. We conduct a classi�cation on international trade �ow
networks with the dataset obtained from the National Bureau ofEconomic Research (h�p://cid.econ.ucdavis.edu/nberus.html). �isdata covers the trade volume and direction information betweencountries of more than 800 di�erent kinds of products which areall encoded by SITC4 digits from 1962 to 2000. We select food andchemicals products as two labels for this experiment, and theirSITC4 encoding starts with 0 and 5 respectively. For example, 0371is for prepared or preserved �sh and 5146 is for oxygen-functionamino-compounds. Fig.5 shows the 2-dimensional representationof the 10 products for two categories. A�er pre-processing, thenumber of the food trade networks is 10705 (including products andproduct combinations with SITC4 digits starting with 0) and thechemicals trade network is 10016 (including products and productcombinations with SITC4 digits starting with 5). �en, we dividethem into training set, validation set and test set according to the ra-tio of 9: 1: 1. During the training, we adjust the network parametersto 15 convolutional �lters in the �rst layer and 30 convolutional �l-ters in the second layer, 300 units of the full-connect layer. Fig.6(b)shows that the classi�cation error rate can be cut down to 5%.
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Figure 6: Plots of loss and validation error rate of the classi-�cation task on BA v.s. WS models (a) and the classi�cationtask for food v.s. chemicals products (b).
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Figure 7: �e dependence of the error rates on the number ofnodes (le�) and the number of edges(right) in the robustnessexperiments. (a) In test set, we set n (number of nodes) =[500, 600, 700, · · · , 1500], and we also retrain n = 800 and n =1200 and test them with the di�erent n test set. (b) In test set,we setm (average number of edges) = [1, 2, 3, · · · , 16], and wealso retrainm = 6 andm = 8 and test themwith the di�erentm test set.
4.3 Robustness on sizes of the networkOur model has good classi�cation performances on both syntheticand empirical data. Next, we want to test the robustness of the
KDD’2018, August 2018, London, United Kingdom Ruyue, X. et al
classi�cation on di�erent sizes (numbers of nodes and edges). Notethat all the experiments performed in classi�cation experimentscontain the model networks with identical numbers of nodes andedges. Nonetheless, a good classi�er should extract the featureswhich are independent on size. �erefore, we examine the robust-ness of the classi�er on various network sizes which are di�erentfrom the training sets. In these experiments, we �rst apply thetrained classi�er for BA and WS networks with n = 1000 nodes andaverage degree < E >= 8 , on new networks di�erent numbers ofnodes and edges. We generate 600 mixed networks by BA and WSmodels with parametersm from [1, 2, 3, · · · , 16] for the BA modeland k from [2, 4, 6, · · · , 32] for the WS model as test set such thattheir average degrees are similar.
We systematically compare how the number of nodes (le�) andedges (right) on the test sets in�uence the error rates as shown inFig.7. At �rst, we observe that the error rates are almost indepen-dent on small �uctuations of the number of nodes. However, theerror rates increase as larger size di�erences are in the test data.�is manifest our classi�ers are robust on the size of the networks.
Nevertheless, there are sudden changes for the variants on thenumber of edges, which indicates that the number of edges haslarger impacts on the network structure. We observe that thereis a sudden drop on error rates with increase ofm for the test setwhen m = 8 for the training set. �rough observing the networkembedding grow we know that he reason behind this sudden changeis the emergence of the multi-center on the representation space forthe BA model. �erefore, the number of links can change the overallstructure in the scale free network, and this makes our classi�erworking worse. Another interesting phenomenon is the error ratescan keep small when the number of edges increase when m in thetraining set is set to 8. �erefore, the classi�ers training on thedense networks are more robust on the variance on edge densities.
5 CONLUSION AND DISCUSSIONIn this paper, we propose a model, which mainly incorporates Deep-Walk and CNN, to solve the network classi�cation problem. WithDeepWalk, we obtain an image for each network, and then we useCNN to complete the classi�cation task. Our method is independenton the number of network samples, which is a big limitation for thekernel methods on graph classi�cation. We validate our model byexperiments with the synthetic data and the empirical data, whichshow that our model performs well in classi�cation tasks. In orderto further understand the network features extracted by our model,we visualize the �lters in CNN and we can see that CNN can cap-ture the di�erences between WS and BA networks. Furthermore,we test the robustness of our model by se�ing di�erent sizes fortraineding and testing. �e biggest advantage of our model is thatour model can deal with networks with di�erent structures andsizes. In addition, the architecture of our model is small and thecomputational complexity is low.
�ere are several potential improvements and extensions to ourmodel that could be addressed as future works. For example, we candevelop more methods to deal with the network features in high-dimensional space. Besides, we think that our model can be appliedto more classi�cation and forecasting tasks in various �elds. Finally,
we believe that extending our model to more graph-structure datawould allow us to tackle a larger variety of problems.
ACKNOWLEDGMENTS�e authors would like to thank the referees for their valuablecomments and helpful suggestions. �e work is supported bythe National Natural Science Foundation of China under GrantNo.: 61673070 and Beijing Normal University InterdisciplinaryProject.
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