Anomaly Detection with Tensor Networks
This work addresses anomaly detection for applications like fraud detection or quality control, but it is incremental as it applies an existing physics-based method to a known machine learning problem.
The paper tackles one-class anomaly detection by using tensor networks to learn a linear transformation in a high-dimensional space, achieving superior performance on tabular datasets and competitive results on image datasets compared to deep and classical algorithms.
Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We exploit the memory and computational efficiency of tensor networks to learn a linear transformation over a space with dimension exponential in the number of original features. The linearity of our model enables us to ensure a tight fit around training instances by penalizing the model's global tendency to a predict normality via its Frobenius norm---a task that is infeasible for most deep learning models. Our method outperforms deep and classical algorithms on tabular datasets and produces competitive results on image datasets, despite not exploiting the locality of images.