Multi-Aspect Heterogeneous Graph Augmentation

Data augmentation has been widely studied as it can be used to improve the generalizability of graph representation learning models. However, existing works focus only on the data augmentation on homogeneous graphs. Data augmentation for heterogeneous graphs remains under-explored. Considering that heterogeneous graphs contain different types of nodes and links, ignoring the type information and directly applying the data augmentation methods of homogeneous graphs to heterogeneous graphs will lead to suboptimal results. In this paper, we propose a novel Multi-Aspect Heterogeneous Graph Augmentation framework named MAHGA. Specifically, MAHGA consists of two core augmentation strategies: structure-level augmentation and metapath-level augmentation. Structure-level augmentation pays attention to network schema aspect and designs a relation-aware conditional variational auto-encoder that can generate synthetic features of neighbors to augment the nodes and the node types with scarce links. Metapath-level augmentation concentrates on metapath aspect, which constructs metapath reachable graphs for different metapaths and estimates the graphons of them. By sampling and mixing up based on the graphons, MAHGA yields intra-metapath and inter-metapath augmentation. Finally, we conduct extensive experiments on multiple benchmarks to validate the effectiveness of MAHGA. Experimental results demonstrate that our method improves the performances across a set of heterogeneous graph learning models and datasets.


INTRODUCTION
Data augmentation as an efective strategy to improve the generalization capability and performance of model has got widespread adoption in various felds such as computer vision (CV) [6,12,34] and natural language processing (NLP) [3,15,16].The core idea of data augmentation is to design various augmentation strategies to generate new plausible data based on existing data without additional ground-truth labels so as to enhance the quantity and/or the quality of existing data.Since graph learning usually faces with many dilemmas such as feature data incompleteness, structural data sparsity brought by power-law distributions, costly data annotations and so on, data augmentation naturally provides a good solution to help graph learning models deal with above problems.However, due to the irregular and non-Euclidean nature of graph data, the structured data augmentation operations used frequently in CV and NLP cannot be applied to graph learning models.Moreover, diferent information modalities and graph properties yield a broader design space for graph data augmentation.Therefore, more and more researchers are starting to pay their attention to the data augmentation for graph data.
Recently, there has been a growing number of works on graph data augmentation [27,30,32,35].Despite their successes, all the current augmentation methods are developed for homogeneous graph and there has never been a work exploring the data augmentation on heterogeneous graphs.Heterogeneous graphs which come with multi-types of nodes and links are ubiquitous in real-world scenarios, ranging from bibliographic networks, social networks to recommendation systems.They usually contain more comprehensive information and richer semantics than homogeneous graphs.Directly adapting homogeneous graph augmentation methods to heterogeneous graph results in the loss of type information and semantics.Moreover, it even introduces unexpected noise which hurts the performance of graph learning models.Consequently, it is important to develop a special data augmentation framework for heterogeneous graphs.
In order to efectively augment heterogeneous graphs, we frst analyse the common challenges faced by heterogeneous graph learning models.On the one hand, besides the data skew caused by the power-law distribution of the graph, there are extremely imbalanced regarding diferent node types because the degree distribution of diferent types of nodes varies dramatically.To verify above phenomena, we depict the degree distribution of diferent nodes of the same type and the average degree distribution of different types of nodes in Figure 1.From the fgure, it is clear that there are signifcant diferences in the degrees of diferent types of nodes.Even for nodes of the same type, the degree distribution is not uniform.Therefore, we argue that the link imbalances between diferent nodes and between diferent types of nodes restrict the performance of heterogeneous graph learning models.Especially, the nodes and the node types with a limited number of links cannot provide sufcient information and become an information bottleneck.
On the other hand, metapath, which describes a composite relation between the node types involved, has been widely used to describe the diverse semantics of a heterogeneous graph.Taking a bibliographic graph as an example, a metapath Paper-Author-Paper (PAP) represents that two papers are written by the same author, while Paper-Subject-Paper (PSP) represents that two papers belong to the same subject.Even though metapath is successful at improving performance by giving a clear guide to heterogeneous graph learning models, existing models get metapath-based node relations from observed heterogeneous graphs.However, the raw observed graphs are usually extracted from complex real-world interaction systems by some predefned rules.They are often noisy or even incomplete due to the inevitably error-prone data measurement or collection.Therefore, obtaining metapath based node relations directly from the observed graph leads to inaccurate results and afects the performance of heterogeneous graph learning models.Furthermore, existing models explicitly ofer the sequences of node types to defne the metapaths which needs sufcient domain knowledge and is difcult to extend.In summary, defning a good set of metapaths and obtaining accurate metapath based node relations are challenging for heterogeneous graph learning models.
In order to tackle the challenges addressed above, we develop a novel Multi-Aspect Heterogeneous Graph Augmentation framework (MAHGA) that contains two aspects of augmentation strategy: structure-level augmentation and metapath-level augmentation.Structure-level augmentation focuses on the local structures of nodes and aims to augment the neighbor information.Specifcally, it designs a relation-aware conditional variational auto-encoder to learn the conditional distribution of neighbor nodes' features given the center node's features and the type of neighbor nodes.By sampling from the learned distribution, we can generate synthetic neighborhood features to augment the nodes and the node types with scarce links.Metapath-level augmentation follows with interest metapath information and employs graphon as a generator to conduct intra-metapath and inter-metapath augmentation.Graphon, a function that determines the matrix of edge probabilities, refects the underlying topology structure of graph so that it is well suited to deal with the challenges in metapath aspect.We frst construct metapath reachable graphs for pre-defned metapaths and estimate the graphons of these graphs.In intra-metapath augmentation, we repeatedly sample from the graphon to generate several new metapath reachable graphs for each metapath.By training heterogeneous graph learning models based on generated and original metapath reachable graphs, MAHGA improves the generalization of heterogeneous graph learning model and alleviates the inaccuracy of metapath caused by the mistakes and incompleteness of observed graph.In inter-metapath augmentation, we draw on the idea of mixup augmentation method which has been widely used in CV feld [28,36,37].By mixing the graphons of metapath reachable graphs of diferent pre-defned metapaths, we can generate many new graphons which imply the new metapaths.What's more, the new metapaths determined by augmented graphons are implicit, meaning that we do not require extra domain knowledge to explicitly defne the node type sequences of them.
In summary, the overall contributions of this paper can be summarized as follow: • We analyse the common challenges faced by heterogeneous graph learning models and use them as the guide to design efective data augmentation strategies for heterogeneous graph.Node-centralized augmentation methods take nodes as basic objects to design augmentation operations.NodeAug [31] designs three augmentation strategies including attribute replacing, edge removing and edge adding for nodes.NASA [2] randomly replaces the immediate neighbors of nodes with their remote neighbors to generate synthetic graph.LA [17] learns the distribution of the node representations of the neighbors conditioned on the central node's representation and generate new neighbor features to augment the central nodes.
Edge-centralized augmentation methods mainly conduct augmentation operations on edges.DropEdge [22] randomly removes a certain number of edges from the original graph at each training epoch.GAUG [40] designs a neural edge predictor to strategically choose ideal edges to add or remove.CFLP [39] employs causal model to create counterfactual edges to improve the model performance.
Graph-centralized augmentation methods directly generate synthetic graphs.MH-Aug [21] defnes an explicit target distribution and draws augmented graphs from the distribution.Suresh et al. [24] employ information bottleneck principle to guide the generation of augmented graphs.MEGA [9] designs a learnable graph augmenter and trains a graph learning model based on a meta-learning paradigm.G-Mixup [11] employs graphon to augment graphs and improve graph classifcation task.
Although above augmentation methods promote the performance of graph learning model, they are only designed for homogeneous graph and ignore the type information and the rich semantics of heterogeneous graph, which are important to heterogeneous graph learning models.

Heterogeneous Graph Representation Learning
Heterogeneous graph representation learning aims to model rich semantics of heterogeneous graph to learn low-dimensional node embedding.CompGCN [25] leverages a variety of entity-relation composition operations from knowledge graph embedding techniques to embed both nodes and relations in a heterogeneous graph.
Inspired by the architecture design of Transformer [26], HGT [13] proposes a heterogeneous mutual attention mechanism and uses it to achieve heterogeneous message passing and aggregation.Simple-HGN [19] combines three well-known techniques: learnable edgetype embedding, residual connections and normalization to design a heterogeneous neighborhood aggregation mechanism.Except for modeling the local structure, there are many works that adopt metapath to capture meaningful semantics.HAN [29] designs node-level attention and semantic-level attention to hierarchically aggregate features from metapath based neighbors and obtain node embedding.MAGNN [8] considers the semantics of intermediate nodes of metapath and designs intra-metapath and inter-metapath aggregation mechanism to acquire node embedding.HPN [14] designs the semantic propagation mechanism and the semantic fusion mechanism to build a more powerful heterogeneous graph learning architecture.

PRELIMINARY
In this section, we frst give formal defnitions of some important terminologies related to heterogeneous graph.Then, we present the heterogeneous graph augmentation problem.Definition 1. Heterogeneous Graph: A heterogeneous graph is defned as a graph G = (V, E) associated with a node type mapping function : V → A and an edge type mapping function : E → R. A and R denote the predefned sets of node types and edge types respectively, with |A| + |R| > 2.
Definition 2. Metapath: A metapath Φ is defned as a path in  In metapath-level augmentation, we frst construct a metapath reachable graph for each pre-defned metapath.Then, we estimate the graphons of these metapath reachable graphs and conduct intra-metapath and inter-metapath augmentation.For intra-metapath augmentation, we use graphon to defne the Bernoulli distribution and resample several synthetic metapath reachable graphs to augment the semantic information of current metapath.For inter-metapath augmentation, we mixup the graphons of metapath reachable graphs of diferent metapaths to generate new graphons which can be regarded as new metapaths.Then, we generate synthetic metapath reachable graphs by sampling from above new graphons to augment the semantic information between metapaths.

Structure-level Augmentation
Structure-level augmentation aims to provide more data to augment the nodes and the node types with scarce links so as to alleviate the sparsity and imbalance issues of heterogeneous graph data.The intuitive solution is to strategically select some nodes as the new neighbors of the central node to augment the local structure of the central node.However, this method has two main drawbacks.1) The good node selection strategy is difcult to defne.Once the inappropriate nodes are selected as the new neighbors, the additional unexpected noise will be introduced to the heterogeneous graph learning model and afect the model performance.2) This method can only select nodes that already exist in the heterogeneous graph as new neighbors to conduct augmentation.However, for the central node, it is possible that there is no appropriate node that can be selected in the heterogeneous graph.Therefore, in order to overcome above limitations, we design a generative model to learn the features' distribution of neighbors and directly sample new neighbors from the distribution rather than select existing nodes as new neighbors.Next, we will elaborate the generative model and the data augmentation process.
4.1.1Relation-aware Conditional Variational Auto-encoder.In a heterogeneous graph, the features of diferent types of nodes are in diferent feature spaces.Therefore, to accurately model the features' distribution of neighbors, it is necessary to consider both the features of the central node and the types of neighbors.Based on the above motivation, we draw on the idea of the conditional variational autoencoder (CVAE) [17,23] to construct the relation-aware conditional variational auto-encoder (RCVAE) as the generative model.Formally, given the features X of the central node and the relation type embedding r , we have ) where X is the features of neighbor of the central node .and are the variational parameters and generative parameters respectively.z is the latent variable which is generated from the prior distribution (z|X , r ).As relation type implies the types of two ends, we employ learnable relation type embedding as the condition in this paper.Then, the evidence lower bound (ELBO) can be written as: ∼ where is the number of neighbors of the central node .z N ( , 2 ) is generated by reparameterization trick.The mean and variance 2 of the distribution are generated by the encoder (X , X , r ) of RCVAE.Finally, we sample a latent variable z ∼ N (0, I) as input for the decoder (z, X , r ) of RCVAE to obtain the synthetic neighbor features X .
where Y is the class labels of downstream task.represents the -th data point in the training dataset.As our augmentation framework uses the original heterogeneous graph data to train RCVAE and employs RCVAE to generate synthetic neighbor features X to conduct augmentation, The likelihood function in Eq.( 3) can be rewritten as follows: X According to the Bayes Rule, we can further decompose in Eq.( 4) as a product of two posterior probabilities: where (Y |X, G) and Ψ (X|G) are the probabilistic distributions approximated by heterogeneous graph learning model and RCVAE respectively.By the decomposition, we decouple the training processes of RCVAE and heterogeneous graph learning model.Therefore, we can pre-train RCVAE frst and then apply it to conduct augmentation.Specifcally, in pre-training stage, we extract neighboring triple (X , X , r ) from the original heterogeneous graph to train RCVAE by maximizing the ELBO (Eq.( 2)).In augmentation stage, we employ RCVAE to generate the synthetic neighbor features and combine them with the original features of the central node as the augmented features of the central node.Finally, we use the augmented features to train various heterogeneous graph learning models so as to improve the performances of these models.

Metapath-level Augmentation
Metapath-level augmentation aims to alleviate the incompleteness and mistake issues in the metapath based sampling (intra-metapath augmentation), while generating new synthetic metapath without extra domain knowledge (inter-metapath augmentation).However, metapath is more complex than the adjacency relation as diferent metapaths contain diferent node types and the length of them varies.It is difcult to design a strategy to directly augment metapath.Consequently, we use metapath based neighbors to transform metapaths into metapath reachable graphs and estimate the graphons of these graphs.Then, we design augmentation strategies operated on graphon to indirectly augment metapath as graphon can maintain the semantics of metapath by modeling the latent structure of metapath reachable graph.Next, we will elaborate more details about metapath-level augmentation.

Graphon Estimation.
Graphon is a nonparametric graph model which characterizes the observed graph and refects its latent graph structure.Mathematically, a graphon is a two-dimensional symmetric Lebesgue measurable function, denoted as where is a measure space, e.g., = [0, 1].As graphon does not have a closed-form expression, how to robustly learn graphon from observed graph becomes a thorny problem.Existing methods mainly depend on the weak regularity lemma of graphon [7] to solve the aforementioned problem, they learn a two-dimensional step function to approximate graphon.The step function W : where = ( 1 , ..., ) partitions the interval [0, 1] into adjacent intervals with a length of 1/.Each , ′ ∈ [0, 1] and the indicator function it is 0. There are many step function learning methods, e.g., the sorting-and-smoothing method (SAS) [4], the stochastic block approximation (SBA) [1], the universal singular value thresholding algorithm (USVT) [5] and so on.In this paper, we employ structured Gromov-Wasserstein barycenters method (SGWB) [33] because it is a computationally-efcient algorithm with solid theoretical guarantee.
More specifcally, we frst defne the squared 2-order Gromov-Wasserstein distance as follows: where are the step functions of two graphs.Vectors 1 and 2 represent the marginal probability measures in partitions.
).The ma-× trix T defnes a transport or coupling between 1 and 2 .⟨•, •⟩ is the inner product of two matrices.
). 1 and 1 are the -dimensional and -dimensional all-one vectors.⊙ represents the Hadamard product.Then, we learn the optimal step function by minimizing the Gromov-Wasserstein distance between the observed graph and step function of the target graphon: where is the number of observed graphs and A is the adjacency matrix of -th observed graph.Given the transports {T } =1 , the above problem has a closed-form solution as follows: graph.(•) sorts the elements of the input vector in descending order and 1 (•) samples values from the input vector via linear interpolation.After obtaining graphon W, we can conduct the intra-metapath and inter-metapath augmentation.

Intra-metapath Augmentation.
Intra-metapath augmentation uses estimated graphon to augment a single metapath.Specifcally, for each metapath, it directly samples new synthetic metapath reachable graphs from graphon.All the generated synthetic graphs refect the semantic information of current metapath.By training heterogeneous graph learning models on the synthetic graphs, intrametapath augmentation can efectively improve the generalization ability of models and alleviate the infuences of data incompleteness and mistake.Formally, for metapath , the sampling process of synthetic metapath reachable graph G can be formulated as follow: where ∼ (0, 1) is the trade-of coefcient to control the contributions from diferent metapaths.W * and G * are the augmented graphon and metapath reachable graph respectively.

Augmentation.
Both of intra-metapath and inter-metapath augmentation generate new synthetic metapath reachable graphs as augmented data.For the heterogeneous graph learning models which require the metapath reachable graph, we directly train models on the synthetic graph.Otherwise, we regard the edges in the synthetic graph as the new types of edges and add them into the original heterogeneous graph, then we train models on the augmented heterogeneous graph.

EXPERIMENTS 5.1 Experimental Setup
5.1.1Datasets.We conduct experiments over three widely used heterogeneous graph datasets.Statistics of them are summarized in Table 1.
• IMDB: IMDB is an online database about movies and television programs.We use a subset of IMDB extracted by [8].It contains 5257 Actors(A), 2081 Directors(D) and 4278 Movies(M).We employ {MAM, MDM} as the pre-defned metapath set.• ACM: ACM is a bibliography website.We adopt an ACM graph provided by [38], containing 7176 Authors(A), 4019 Papers(P) and 60 Subjects.We employ {PSP, PAP} as the pre-defned metapath set.• Yelp: Yelp is a social network which contains a large amount of user comment data.Here, we adopt the subset of Yelp constructed by [18].It comprises 2614 businesses(B), 1286 users(U), 4 services(S) and 9 rating levels(L).We employ {BUB, BSB, BUBLB, BUBSB} as the pre-defned metapath set.

Baselines.
As there is no graph augmentation method for heterogeneous graphs, we select six state-of-the-art homogeneous graph augmentation methods as baselines and adapt them to heterogeneous graphs.The details of baselines are as follows: • Node-centralized Augmentation: We select NodeAug [31], NASA [2] and LA [17] as baselines.NodeAug proposes three node augmentation strategies and we only apply these strategies to target nodes which the downstream task pays attention to.NASA replaces the immediate neighbors of nodes with their remote neighbors and we independently conduct above operation on diferent types of neighbors to achieve augmentation.LA learns the features' distribution of neighbors to generate augmented data and we also use it to augment target nodes.• Edge-centralized Augmentation: We select DropEdge [22] and GAUG [40] as baselines.DropEdge randomly removes edges to augment the graph and we apply it to all types of edges.For GAUG, we construct multiple edge predictors to independently add or remove diferent types of edges.• Graph-centralized Augmentation: We select MH-Aug [21] as baseline.As MH-Aug directly samples synthetic graphs from the target distribution, we construct diferent distribution for diferent types of edges to generate the augmented data.

Implementation.
For all baselines, we tune the hyperparameters based on the validation set performance.For MAHGA, we employ two-layer-MLPs as the encoder and decoder of RCVAE, other model parameters such as the dimensions of relation type embedding r and latent variable z, the pre-training setting of RCVAE, the number of samples in structure-level and metapathlevel augmentation and the number of mixups in inter-metapath augmentation are tuned by grid search.What's more, we utilize the open-source toolkit OpenHGNN [10] to implement the backbone models and the models parameters keep their reported optimal values.

Performance Comparison
We employ node classifcation as a downstream task to evaluate the impact of diferent graph augmentation methods on the performance of backbone models.The results are shown in Table 2. From the table, we make the following observations.Firstly, although some homogeneous graph augmentation baselines can improve the performance of special backbone models on special heterogeneous datasets, there is no one baseline that can be applied to all backbone models to have a positive impact on all datasets.Especially on ACM dataset, all augmentation methods fail to promote MAGNN but even degrade its performance.The results indicate that homogeneous graph augmentation methods cannot generate the satisfed augmented data to efectively improve the generalization and modeling ability of heterogeneous graph learning models.So, directly adapting homogeneous graph augmentation method to heterogeneous graph is not a good solution and it is necessary to design a specialized augmentation framework for heterogeneous graphs.Secondly, in most instances, node-centralized augmentation methods perform worse than edge-centralized augmentation methods and graph-centralized augmentation method.Some typical nodecentralized augmentation methods such as LA even severely harm the performances of backbone models.We attribute the results to that node-centralized augmentation methods are more fne-grained and they pay more attention to the local information of graphs.However, in heterogeneous graphs, the local information is more abundant than that in homogeneous graphs as diferent types of nodes have diferent feature spaces and the local structures of them are also various.Node-centralized homogeneous graph augmentation methods do not fully consider above characteristics of hetero- geneous graphs in the augmentation process so that they cannot perform as well as they do on homogeneous graphs.Finally, our augmentation framework MAHGA signifcantly and consistently outperforms all baselines on all backbone models and datasets.In general, MAHGA achieves relative performance gains over original backbone models by 0.58-3.88% in terms of Micro-F1 and 0.87-5.4% in terms of Macro-F1, which proves the efectiveness and superiority of MAHGA.By designing sophisticated augmentation strategies from network schema aspect and metapath aspect, MAHGA introduces the heterogeneity and semantics of heterogeneous graphs into augmentation process, which help to generate better augmented data to improve the performances of heterogeneous graph learning models.

Ablation Study
In order to verify the efectiveness of diferent augmentation strategies of MAHGA, we design three variants of MAHGA to conduct the ablation experiments.Only one augmentation strategy is available for each variant.For example, "+Structure-level" means that this variant of MAHGA only employs the structure-level augmentation strategy in Section 4.1.The experimental results are shown in Table 3. Due to the limitation of space, we only display the results on ACM dataset.Other results are similar so we omit them.
As we can observe, all augmentation strategies of MAHGA have a positive impact and they improve the performances of backbone  models.However, for diferent backbone models and datasets, the efects of diferent augmentation strategies vary.For example, the performance improvements of MAGNN and HGT by metapathlevel augmentation are not as signifcant as that by structure-level augmentation, while metapath-level augmentation performs better than structure-level augmentation on HAN and HPN.It is because MAGNN and HGT require complete path information including the intermediate nodes along the metapath, but HAN and HPN explicitly utilize the metapath based neighbors.Despite all this, MAHGA still outperforms all variants which indicates that diferent augmentation strategies augment heterogeneous graph from diferent aspects and combining them together can further improve the augmentation efect.

Visualization
For a more intuitive comparison and to further show the efectiveness of our proposed augmentation framework, we select HAN as backbone model and conduct the task of visualization on three datasets.Here, we utilize t-SNE [20] to project the node representation learned by HAN into a 2-dimensional space.The experimental results are depicted in Figure 3. "Yelp_ori" means that we directly train HAN on Yelp dataset, while "Yelp_aug" means that we employ MAHGA in the training of HAN.From the visualization, we can see that the learned node representations have the higher intra-class similarity and the clearer distinct boundary among diferent classes when we adopt MAHGA to train HAN.It is a solid evidence to prove that MAHGA can enhance the backbone models well.

CONCLUSION
In this paper, we study the data augmentation on heterogeneous graphs, where node types and link types are diverse.Unfortunately, existing graph augmentation methods are only designed for homogeneous graphs and they cannot perform well on heterogeneous graphs because they ignore the type information and rich semantics in the latter.Therefore, we propose MAHGA, a novel heterogeneous graph augmentation framework to address the above issues.MAHGA designs augmentation strategies from network schema and metapath aspects to fully consider the heterogeneity and semantics.Extensive experiments on three common heterogeneous datasets and six popular heterogeneous graph learning models demonstrate the rationality and efectiveness of MAHGA.

Figure 1 :
Figure 1: The distribution of node degree on yelp dataset.(a) depicts the degree distribution of diferent business nodes.(b) depicts the average degree distribution of diferent types of nodes.

1 between objects 1 Definition 3 .Definition 4 .Definition 5 .
and , where • denotes the composition operation on relations.Metapath based Neighbors: Given a node and a metapath Φ in a heterogeneous graph G, the metapath Φ based neighbors N Φ of node are defned as the set of nodes which connect with node via metapath Φ. Metapath Reachable Graph: Given a metapath Φ in a heterogeneous graph G, the metapath reachable graph G Φ is constructed by all the metapath Φ based neighbor pairs in graph G.Note that G Φ is homogeneous if Φ is symmetric.Heterogeneous Graph Augmentation: Given a heterogeneous graph G = (V, E), heterogeneous graph augmentation aims to fnd a mapping function : G → G such that the augmented graph G = (V, E) can be used to improve the generalization ability of a heterogeneous graph learning model.

Figure 2 :
Figure 2: The overall framework of the proposed MAHGA

4. 1 . 2
Pre-training and Augmentation.In general, for a specifc downstream task, We can use Maximum Likelihood Estimation (MLE) to estimate the parameter of a heterogeneous graph learning model.It optimizes the following likelihood function: Ö (Y |G)

Figure 3 :
Figure 3: 2D visualization of node representation of HAN on three datasets using t-SNE.The diferent colors represent diferent classes.

Table 1 :
Statistics of datasets.Inter-metapath Augmentation.The core idea of inter-metapath augmentation is to create new synthetic metapaths based on predefned metapaths.As graphon models the metapath reachable graph, it can represent the corresponding metapath.Therefore, we directly generate the graphons of new synthetic metapaths to avoid explicitly defning the node types sequence.Concretely, we employ mixup technology to interpolate the graphons of metapath reachable graphs of pre-defned metapaths to generate new graphons.Each augmented graphon represents an implicit synthetic metapath.Then, we sample metapath reachable graphs from the augmented graphons to train heterogeneous graph learning models.The augmentation process can be denoted as follow:

Table 3 :
Ablation study on ACM dataset.The best results are Bold.(•) represents the improvement of performance comparing with the original backbone model.