# Unsupervised Anomaly Detection via Nonlinear Manifold Learning

arXiv: https://arxiv.org/abs/2306.09441 · HTML: https://mlsanity.com/paper/2306.09441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Autoencoders for Unsupervised Anomaly Segmentation in Brain MR Images: A Comparative Study](https://mlsanity.com/paper/2004.03271/) (2020)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [Deep Learning for Unsupervised Anomaly Localization in Industrial Images: A Survey](https://mlsanity.com/paper/2207.10298/) (2022)
- [Toward Deep Supervised Anomaly Detection: Reinforcement Learning from Partially Labeled Anomaly Data](https://mlsanity.com/paper/2009.06847/) (2020)
- [Unsupervised and Semi-supervised Anomaly Detection with LSTM Neural Networks](https://mlsanity.com/paper/1710.09207/) (2017)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Clustering and Unsupervised Anomaly Detection with L2 Normalized Deep Auto-Encoder Representations](https://mlsanity.com/paper/1802.00187/) (2018)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Data Fusion with Latent Map Gaussian Processes](https://mlsanity.com/paper/2112.02206/) (2021)
- [Anomaly Detection in High Dimensional Data](https://mlsanity.com/paper/1908.04000/) (2019)

## Abstract (arXiv)

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty detection. The majority of existing anomaly detection methods either are exclusively developed for (semi) supervised settings, or provide poor performance in unsupervised applications where there is no training data with labeled anomalous samples. To bridge this research gap, we introduce a robust, efficient, and interpretable methodology based on nonlinear manifold learning to detect anomalies in unsupervised settings. The essence of our approach is to learn a low-dimensional and interpretable latent representation (aka manifold) for all the data points such that normal samples are automatically clustered together and hence can be easily and robustly identified. We learn this low-dimensional manifold by designing a learning algorithm that leverages either a latent map Gaussian process (LMGP) or a deep autoencoder (AE). Our LMGP-based approach, in particular, provides a probabilistic perspective on the learning task and is ideal for high-dimensional applications with scarce data. We demonstrate the superior performance of our approach over existing technologies via multiple analytic examples and real-world datasets.