When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
Graph-structured data is ubiquitous across diverse domains, including social networks, recommendation systems, biology, and transportation networks. The analysis of such intricate data presents considerable challenges. Graph neural network, with its proficiency in capturing complex relationships within graphs, has emerged as a potent paradigm. Within this framework, graph convolutional networks have attracted substantial interest due to their ability to acquire informative node representations through iterative aggregation of information from neighboring nodes. These networks have paved the way for various applications such as node classification, link prediction and anomaly detection.
In this thesis, we present a novel approach for enhancing semi-supervised node classification on graph-structured data. The proposed framework addresses the challenges of oversmoothing and shrinking effects by introducing a nonlinear smoothness term into the feature diffusion mechanism of convolutional neural networks. We conducted comprehensive experiments on diverse benchmark datasets demonstrating that our approach consistently outperforms or matches state-of the-art baseline methods. Moreover, we also introduce an innovative approach to semi-supervised anomaly detection on graph-structured data using graph fairing convolutional networks. This approach leverages a novel update rule inspired by implicit fairing, derived directly from the Jacobi iterative method. The model 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 demonstrate the superior performance of our proposed model compared to existing state-of-the-art methods in the field of anomaly detection. In addition, we propose a novel approach to unsupervised anomaly detection in graph data by leveraging a graph encoder-decoder architecture and a specialized 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 model outperforms existing methods.