Anomaly Detection from a Tensor Train Perspective

TL;DR

A series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation, which consist of preserving the structure of normal data in compression and deleting the structure of anomalous data.

Abstract

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.

Figures (13)

• Figure 1: a) Tensor $T$ of order 5 in tensor networks notation, b) TT representation of a tensor of order 5 in tensor networks notation
• Figure 2: Process of creation of the TT representation for a tensor of order 5, following the described steps.
• Figure 3: Example of the TT representation generation process for the data to be tested.
• Figure 4: AUROC results obtained with ACGCTNAD for different $\tau$ values considering each type of digit as normal and all others as anomalous. In green we mark the maximum possible value ($1$) and in red the value $0.5$.
• Figure 5: Maximum AUROC achieved with ACGCTNAD for each type of digit. In green we mark the maximum possible value ($1$) and in red the minimum possible value ($0.5$).