We present a series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation. These algorithms consist of preserving the structure of normal data in compression and deleting the structure of anomalous data. The algorithms can be applied to any tensor network representation. We test the effectiveness of the methods with digits and Olivetti faces datasets and a cybersecurity dataset to determine cyber-attacks.

翻译：我们提出一系列基于张量网络的异常检测算法，通过张量列表示中的数据压缩实现异常检测。这些算法的核心思想是在数据压缩过程中保留正常数据的结构特征，同时消除异常数据的结构信息。该算法可适用于任意张量网络表示。我们通过手写数字数据集、Olivetti人脸数据集以及网络安全数据集验证了该方法的有效性，用以识别网络攻击行为。