AD-DMKDE: Anomaly Detection through Density Matrices and Fourier Features

TL;DR

This paper introduces AD-DMKDE, a novel anomaly detection method leveraging density matrices and Fourier features, offering efficient training, constant prediction complexity, and competitive performance across diverse datasets.

Contribution

The paper proposes a new anomaly detection approach combining density matrices and Fourier features, providing an efficient approximation of KDE with scalable and hardware-friendly architecture.

Findings

Competitive performance on benchmark datasets

Constant prediction complexity relative to data size

Efficient training with optimized data embedding parameters

Abstract

This paper presents a novel density estimation method for anomaly detection using density matrices (a powerful mathematical formalism from quantum mechanics) and Fourier features. The method can be seen as an efficient approximation of Kernel Density Estimation (KDE). A systematic comparison of the proposed method with eleven state-of-the-art anomaly detection methods on various data sets is presented, showing competitive performance on different benchmark data sets. The method is trained efficiently and it uses optimization to find the parameters of data embedding. The prediction phase complexity of the proposed algorithm is constant relative to the training data size, and it performs well in data sets with different anomaly rates. Its architecture allows vectorization and can be implemented on GPU/TPU hardware.