Random Walks-based Anomaly Detection (RWAD) is commonly used to identify anomalous patterns in various applications. An intriguing characteristic of RWAD is that the input graph can either be pre-existing or constructed from raw features. Consequently, there are two potential attack surfaces against RWAD: graph-space attacks and feature-space attacks. In this paper, we explore this vulnerability by designing practical dual-space attacks, investigating the interplay between graph-space and feature-space attacks. To this end, we conduct a thorough complexity analysis, proving that attacking RWAD is NP-hard. Then, we proceed to formulate the graph-space attack as a bi-level optimization problem and propose two strategies to solve it: alternative iteration (alterI-attack) or utilizing the closed-form solution of the random walk model (cf-attack). Finally, we utilize the results from the graph-space attacks as guidance to design more powerful feature-space attacks (i.e., graph-guided attacks). Comprehensive experiments demonstrate that our proposed attacks are effective in enabling the target nodes from RWAD with a limited attack budget. In addition, we conduct transfer attack experiments in a black-box setting, which show that our feature attack significantly decreases the anomaly scores of target nodes. Our study opens the door to studying the dual-space attack against graph anomaly detection in which the graph space relies on the feature space.

翻译：基于随机游走的异常检测（RWAD）常用于识别各类应用中的异常模式。RWAD的一个显著特征是输入图既可以预先存在，也可以从原始特征构建。因此，RWAD面临两种潜在的攻击面：图空间攻击和特征空间攻击。本文通过设计实用的双空间攻击来探索这一脆弱性，研究图空间攻击与特征空间攻击之间的交互作用。为此，我们进行了彻底的复杂性分析，证明攻击RWAD是NP困难的。随后，我们将图空间攻击表述为双层优化问题，并提出两种求解策略：交替迭代（alterI攻击）或利用随机游走模型的闭式解（cf攻击）。最后，我们利用图空间攻击的结果作为指导，设计更强大的特征空间攻击（即图引导攻击）。大量实验表明，我们提出的攻击能够在有限的攻击预算下有效使RWAD的目标节点被绕过。此外，我们在黑盒设置下进行了迁移攻击实验，结果显示我们的特征攻击显著降低了目标节点的异常分数。本研究为针对图异常检测（其中图空间依赖于特征空间）的双空间攻击研究打开了大门。