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.

翻译：图神经网络（GNN）的关键组成部分之一是池化操作，旨在缩小图的规模同时保留重要的结构信息。然而，现有的大多数图池化策略依赖于通过使用GNN层获得的分配矩阵，该矩阵具有可训练参数，通常会导致显著的计算复杂性且池化过程缺乏可解释性。本文提出一种无监督的图编码器-解码器模型，通过学习异常评分函数根据节点的异常程度进行排序，从而检测图中的异常节点。在编码阶段，我们设计了一种新颖的池化机制LCPool，该机制利用局部约束线性编码进行特征编码，通过求解带有局部正则化项的最小二乘优化问题来获得聚类分配矩阵。通过在编码过程中施加局部约束，LCPool无需可学习参数，能够高效处理大规模图，并在保留图最关键结构特征的同时有效生成粗化图表示。在解码阶段，我们提出一种逆池化操作LCUnpool，用于重构原始图的结构和节点特征。我们在六个基准数据集上使用多种评估指标对方法进行实证评估，结果证明了其相较于现有最先进异常检测方法的优越性。