Graph convolutional networks gain remarkable success in semi-supervised learning on graph-structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph structure. Previous methods, spectral methods and spatial methods, devote to defining graph convolution as a weighted average over neighboring nodes, and then learn graph convolution kernels to leverage the smoothness to improve the performance of graph-based semi-supervised learning. One open challenge is how to determine appropriate neighborhood that reflects relevant information of smoothness manifested in graph structure. In this paper, we propose GraphHeat, leveraging heat kernel to enhance low-frequency filters and enforce smoothness in the signal variation on the graph. GraphHeat leverages the local structure of target node under heat diffusion to determine its neighboring nodes flexibly, without the constraint of order suffered by previous methods. GraphHeat achieves state-of-the-art results in the task of graph-based semi-supervised classification across three benchmark datasets: Cora, Citeseer and Pubmed.

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Consumer loans, i.e., loans to finance consumers to buy certain types of expenditures, is increasingly popular in e-commerce platform. Different from traditional loans with mortgage, online consumer loans only take personal credit as collateral for loans. Consequently, loan fraud detection is particularly critical for lenders to avoid economic loss. Previous methods mainly leverage applicant's attributes and historical behavior for loan fraud detection. Although these methods gain success at detecting potential charge-offs, yet they perform worse when multiple persons with various roles (e.g., sellers, intermediaries) collude to apply fraudulent loan. To combat this challenge, we consider the problem of loan fraud detection via exploiting roles of users and multi-type social relationships among users. We propose a novel Graph neural network with a Role-constrained Conditional random field, namely GRC, to learn the representation of applicants and detect loan fraud based on the learned representation. The proposed model characterizes the multiple types of relationships via self-attention mechanism and employs conditional random field to constrain users with the same role to have similar representation. We validate the proposed model through experiments in large-scale auto-loan scenario. Extensive experiments demonstrate that our model achieves state-of-the-art results in loan fraud detection on Alipay, one online credit payment service serving more than 450 million users in China.