A New Tensor Summary Statistic for Real-Time Detection of Stealthy Anomaly in Avatar Interaction

Avatar is one of the most intuitive central components in Metaverse and faces serious security problems, particularly during the interaction with each other. In this article, we consider the problem of timely detecting the stealthy anomaly in the avatar interaction, which is crucial for security and privacy in Metaverse. With this goal, a new tensor summary statistic is proposed first to well depict the statistical discrepancy between normal and anomalous interaction volume samples, even when anomalies are stealthy. The proposed tensor summary statistic is established from the tensor linear representation residual, which naturally implies the statistical probability that an interaction volume sample lies within or deviates from the tensor lateral space. Moreover, a convex optimization programme is introduced to robustly recover the tensor lateral space in the presence of anomalous samples, thereby enhancing the robustness of our tensor summary statistic. On the basis of the tensor summary statistic, a non-parametric statistic framework is developed for the real-time detection of the stealthy interaction volume anomaly. We also provide theoretical analysis concerning its detection performance and parameter selection. Extensive experiments using synthetic and real-world datasets verify our effectiveness and superiority. Compared with benchmark methods, the proposed detection scheme achieves significantly lower detection delay and higher false alarm period, particularly in the detection of stealthy anomalies with a low change rate.