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

arXiv: https://arxiv.org/abs/2210.14796 · HTML: https://mlsanity.com/paper/2210.14796/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Quantum Adaptive Fourier Features for Neural Density Estimation](https://mlsanity.com/paper/2208.00564/) (2022)

## Built on by (most cited first, 5 of 5)

- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)
- [PIP: Positional-encoding Image Prior](https://mlsanity.com/paper/2211.14298/) (2022)
- [LEAN-DMKDE: Quantum Latent Density Estimation for Anomaly Detection](https://mlsanity.com/paper/2211.08525/) (2022)
- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)
- [On Multi-entity, Multivariate Quickest Change Point Detection](https://mlsanity.com/paper/2509.18310/) (2025)

## Abstract (arXiv)

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.