Mahsa Mesgaran

Mahsa Mesgaran, A. Ben Hamza

A key component of many graph neural networks (GNNs) is the pooling operation, which seeks to reduce the size of a graph while preserving important structural information. However, most existing graph pooling strategies rely on an assignment matrix obtained by employing a GNN layer, which is characterized by trainable parameters, often leading to significant computational complexity and a lack of interpretability in the pooling process. In this paper, we propose an unsupervised graph encoder-decoder model to detect abnormal nodes from graphs by learning an anomaly scoring function to rank nodes based on their degree of abnormality. In the encoding stage, we design a novel pooling mechanism, named LCPool, which leverages locality-constrained linear coding for feature encoding to find a cluster assignment matrix by solving a least-squares optimization problem with a locality regularization term. By enforcing locality constraints during the coding process, LCPool is designed to be free from learnable parameters, capable of efficiently handling large graphs, and can effectively generate a coarser graph representation while retaining the most significant structural characteristics of the graph. In the decoding stage, we propose an unpooling operation, called LCUnpool, to reconstruct both the structure and nodal features of the original graph. We conduct empirical evaluations of our method on six benchmark datasets using several evaluation metrics, and the results demonstrate its superiority over state-of-the-art anomaly detection approaches.

Mahsa Mesgaran, A. Ben Hamza

Graph convolutional networks learn effective node embeddings that have proven to be useful in achieving high-accuracy prediction results in semi-supervised learning tasks, such as node classification. However, these networks suffer from the issue of over-smoothing and shrinking effect of the graph due in large part to the fact that they diffuse features across the edges of the graph using a linear Laplacian flow. This limitation is especially problematic for the task of node classification, where the goal is to predict the label associated with a graph node. To address this issue, we propose an anisotropic graph convolutional network for semi-supervised node classification by introducing a nonlinear function that captures informative features from nodes, while preventing oversmoothing. The proposed framework is largely motivated by the good performance of anisotropic diffusion in image and geometry processing, and learns nonlinear representations based on local graph structure and node features. The effectiveness of our approach is demonstrated on three citation networks and two image datasets, achieving better or comparable classification accuracy results compared to the standard baseline methods.

Mahsa Mesgaran, A. Ben Hamza

Graph convolution is a fundamental building block for many deep neural networks on graph-structured data. In this paper, we introduce a simple, yet very effective graph convolutional network with skip connections for semi-supervised anomaly detection. The proposed layerwise propagation rule of our model is theoretically motivated by the concept of implicit fairing in geometry processing, and comprises a graph convolution module for aggregating information from immediate node neighbors and a skip connection module for combining layer-wise neighborhood representations. This propagation rule is derived from the iterative solution of the implicit fairing equation via the Jacobi method. In addition to capturing information from distant graph nodes through skip connections between the network's layers, our approach exploits both the graph structure and node features for learning discriminative node representations. These skip connections are integrated by design in our proposed network architecture. The effectiveness of our model is demonstrated through extensive experiments on five benchmark datasets, achieving better or comparable anomaly detection results against strong baseline methods. We also demonstrate through an ablation study that skip connection helps improve the model performance.