# Latent Anomaly Detection Through Density Matrices

arXiv: https://arxiv.org/abs/2408.07623 · HTML: https://mlsanity.com/paper/2408.07623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Adversarially Learned Anomaly Detection](https://mlsanity.com/paper/1812.02288/) (2018)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Anomaly Detection With Conditional Variational Autoencoders](https://mlsanity.com/paper/2010.05531/) (2020)
- [Anomaly Detection in Medical Imaging -- A Mini Review](https://mlsanity.com/paper/2108.11986/) (2021)
- [Robust Unsupervised Video Anomaly Detection by Multi-Path Frame Prediction](https://mlsanity.com/paper/2011.02763/) (2020)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Explainable Contextual Anomaly Detection using Quantile Regression Forests](https://mlsanity.com/paper/2302.11239/) (2023)
- [Quantum Adaptive Fourier Features for Neural Density Estimation](https://mlsanity.com/paper/2208.00564/) (2022)

## Abstract (arXiv)

This paper introduces a novel anomaly detection framework that combines the robust statistical principles of density-estimation-based anomaly detection methods with the representation-learning capabilities of deep learning models. The method originated from this framework is presented in two different versions: a shallow approach employing a density-estimation model based on adaptive Fourier features and density matrices, and a deep approach that integrates an autoencoder to learn a low-dimensional representation of the data. By estimating the density of new samples, both methods are able to find normality scores. The methods can be seamlessly integrated into an end-to-end architecture and optimized using gradient-based optimization techniques. To evaluate their performance, extensive experiments were conducted on various benchmark datasets. The results demonstrate that both versions of the method can achieve comparable or superior performance when compared to other state-of-the-art methods. Notably, the shallow approach performs better on datasets with fewer dimensions, while the autoencoder-based approach shows improved performance on datasets with higher dimensions.