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 graphs or feature-derived graphs 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 coupled-space (interdependent feature-space and graph-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 to evade the detection 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 coupled-space attack against graph anomaly detection in which the graph space relies on the feature space.

中文翻译：

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针对基于随机游走的异常检测的耦合空间攻击


基于随机游走的异常检测 （RWAD） 通常用于识别各种应用中的异常模式。RWAD 的一个有趣特征是，输入图可以是预先存在的图，也可以是从原始特征构建的特征派生图。因此，针对 RWAD 的两个潜在攻击面：图形空间攻击和特征空间攻击。在本文中，我们通过设计实用的耦合空间（相互依赖的特征空间和图空间）攻击来探索这一漏洞，研究图空间和特征空间攻击之间的相互作用。为此，我们进行了全面的复杂性分析，证明攻击 RWAD 是 NP 困难的。然后，我们继续将图空间攻击表述为一个双层优化问题，并提出两种策略来解决它：替代迭代（alterI-attack）或利用随机游走模型的封闭式解决方案（cf-attack）。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（即图导攻击）。综合实验表明，我们提出的攻击可以有效地使目标节点以有限的攻击预算逃避 RWAD 的检测。此外，我们在黑盒设置下进行了传输攻击实验，结果表明我们的特征攻击显著降低了目标节点的异常分数。我们的研究为研究针对图异常检测的耦合空间攻击打开了大门，其中图空间依赖于特征空间。