## 1 Introduction  
With the rapid developments of social networks, communication networks, biological networks, and other applications in various fields, the scale of graph data grows sharply. Attributed graphs as the basic data representation contain a large number of node attributes and connection relationships, but it is difficult to perform node classification due to the massive nodes and complicated topology. How to mine the inherent information hidden in the attributed graph without the prior knowledge is a challenging task.  
Attributed graph clustering aims to group nodes into different clusters by exploiting node attributes and graph structures sufficiently, where relevant nodes are assigned to the same cluster and the difference between clusters is maximized. By leveraging node attributes and structural information, attributed graph clustering is mainly summarized in three main categories as follows.  
Attribute-based clustering such as spectral clustering only respects node attributes and performs clustering on the similarity matrix with node attributes directly. In comparison, structure-based clustering just explores vertex connectivity by manipulating the adjacency matrix of the attributed graph, e.g., random walk [1], Laplacian eigenmaps [2]. However, the above two kinds of graph clustering methods lack incorporated node features and a mining topological structure.  
In recent years, generative models based on graph convolutional network (GCN [3]) has been widely studied for attributed graph clustering, where GCN [3] updates the node representation by incorporating neighbor node features to construct graph embedding. Classic generative models include variational graph auto-encoder (VGAE) [4], marginalized graph autoencoder (MGAE) [5], and adversarially regularized graph autoencoder (ARGE) [6]. These methods have been demonstrated as being very practical for performing clustering by unifying graph structures and attributing information. However, graph clustering via GCN [3], such as VGAE [4] or MGAE [5], simply employs shadow two-layer or three-layer graph convolution respectively, which only leverages two or three-hop neighborhood features, and it is hard to capture global structural information. On the contrast, stacking too many layers may lead to over-smoothing and complex computation.  
[PERSON] et al. [7] adopt adaptive graph convolution (AGC) as a low-pass graph filter to make node features smoother. Nevertheless, AGC [7] might not determine the appropriate neighborhood that reflects the relevant information of connected nodes represented in graph structures.  
To overcome the above difficulty, we propose an adaptive graph convolution model using heat kernel (AGCHK) to obtain an appropriate neighborhood of the center node and enhance the ability to capture graph smoothness. Our contributions can be summarized as follows:  
* We replace the weak linear low-pass filter in standard AGC [7] by heat kernel to enhance the low-pass characteristics of the graph filter.
* We leverage the scaling parameter to restrict the neighborhood of the center node, which is flexible to exploit distant-distance nodes while excluding some irrelevant close-distance nodes.
* We choose the Davies-Bouldin index (DBI) as the criterion to evaluate the cluster quality, which can exactly determine the order of adaptive graph convolution.
* Experimental results show that AGCHK is obviously superior to other compared methods in the task of attribute graph clustering on benchmark datasets such as Cora, Citeseer, Pubmed, and Wiki.