Abstract

Graph-structured data is ubiquitous across diverse domains, including social networks, recommendation systems, brain networks, computational chemistry, biology, sensor networks, and transportation networks. Graph neural networks have recently emerged as a powerful paradigm for the analysis of graph-structured data due to their ability to effectively capture complex relationships and learn expressive graph node representations through iterative aggregation of information from neighboring nodes. These learned representations can then be used in various downstream tasks such as node classification and anomaly detection.
In this thesis, we introduce a graph representation learning model for semi-supervised node classification.
The proposed feature-preserving model addresses the challenges of oversmoothing and shrinking effects by introducing a nonlinear smoothness term into the feature diffusion mechanism
of graph convolutional networks. We conduct comprehensive experiments on diverse benchmark datasets demonstrating that our approach consistently outperforms or matches state-of-the-art baseline methods. Inspired by the concept of implicit fairing in geometry processing, we also propose a graph fairing convolutional network architecture for semi-supervised anomaly detection. The proposed model leverages a feature propagation rule derived directly from the Jacobi iterative method and incorporates skip connections between initial node features and each hidden layer, facilitating robust information propagation throughout the network. Our extensive experiments on five benchmark datasets showcase the superior performance of our graph fairing convolutional network
compared to existing anomaly detection methods. In addition, we propose an unsupervised anomaly detection approach on graph-structured data by designing a graph encoder-decoder architecture
and a locality-constrained pooling strategy. This pooling mechanism extracts local patterns and reduces the impact of irrelevant global graph information, enhancing the discriminative power of the learned features. In the decoding phase, an unpooling operation followed by a graph deconvolutional network reconstructs the graph data. Extensive experiments on six benchmark datasets demonstrate that our graph encoder-decoder model outperforms competitive baseline methods.