# Robust Subspace Recovery Layer for Unsupervised Anomaly Detection

arXiv: https://arxiv.org/abs/1904.00152 · HTML: https://mlsanity.com/paper/1904.00152/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2019.

## Built on by (most cited first, 30 of 31)

- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [One-Class Classification: A Survey](https://mlsanity.com/paper/2101.03064/) (2021)
- [Self-supervise, Refine, Repeat: Improving Unsupervised Anomaly Detection](https://mlsanity.com/paper/2106.06115/) (2021)
- [Adaptive Model Pooling for Online Deep Anomaly Detection from a Complex Evolving Data Stream](https://mlsanity.com/paper/2206.04792/) (2022)
- [Unsupervised Outlier Detection using Memory and Contrastive Learning](https://mlsanity.com/paper/2107.12642/) (2021)
- [Anomaly Detection: How to Artificially Increase your F1-Score with a Biased Evaluation Protocol](https://mlsanity.com/paper/2106.16020/) (2021)
- [METER: A Dynamic Concept Adaptation Framework for Online Anomaly Detection](https://mlsanity.com/paper/2312.16831/) (2023)
- [Enhancing Unsupervised Anomaly Detection with Score-Guided Network](https://mlsanity.com/paper/2109.04684/) (2021)
- [Probabilistic Robust Autoencoders for Outlier Detection](https://mlsanity.com/paper/2110.00494/) (2021)
- [ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models](https://mlsanity.com/paper/2301.04257/) (2023)
- [Normality-Calibrated Autoencoder for Unsupervised Anomaly Detection on Data Contamination](https://mlsanity.com/paper/2110.14825/) (2021)
- [Towards an Awareness of Time Series Anomaly Detection Models' Adversarial Vulnerability](https://mlsanity.com/paper/2208.11264/) (2022)
- [Revisiting Deep Feature Reconstruction for Logical and Structural Industrial Anomaly Detection](https://mlsanity.com/paper/2410.16255/) (2024)
- [Robust Vector Quantized-Variational Autoencoder](https://mlsanity.com/paper/2202.01987/) (2022)
- [An Iterative Method for Unsupervised Robust Anomaly Detection Under Data Contamination](https://mlsanity.com/paper/2309.09436/) (2023)
- [Unsupervised Anomaly Detection for Auditing Data and Impact of Categorical Encodings](https://mlsanity.com/paper/2210.14056/) (2022)
- [GRAM: An Interpretable Approach for Graph Anomaly Detection using Gradient Attention Maps](https://mlsanity.com/paper/2311.06153/) (2023)
- [SLA2P: Self-supervised Anomaly Detection with Adversarial Perturbation](https://mlsanity.com/paper/2111.12896/) (2021)
- [Detecting Abnormal Operations in Concentrated Solar Power Plants from Irregular Sequences of Thermal Images](https://mlsanity.com/paper/2406.16077/) (2024)
- [FiSH: Fair Spatial Hotspots](https://mlsanity.com/paper/2106.06049/) (2021)
- [TPAD: Identifying Effective Trajectory Predictions Under the Guidance of Trajectory Anomaly Detection Model](https://mlsanity.com/paper/2201.02941/) (2022)
- [Repairing Systematic Outliers by Learning Clean Subspaces in VAEs](https://mlsanity.com/paper/2207.08050/) (2022)
- [Unsupervised Deep One-Class Classification with Adaptive Threshold based on Training Dynamics](https://mlsanity.com/paper/2302.06048/) (2023)
- [A Robust Autoencoder Ensemble-Based Approach for Anomaly Detection in Text](https://mlsanity.com/paper/2405.13031/) (2024)
- [Diminishing Empirical Risk Minimization for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2205.14676/) (2022)
- [Anomaly segmentation model for defects detection in electroluminescence images of heterojunction solar cells](https://mlsanity.com/paper/2208.05994/) (2022)
- [MSS-PAE: Saving Autoencoder-based Outlier Detection from Unexpected Reconstruction](https://mlsanity.com/paper/2304.00709/) (2023)
- [Rethinking Unsupervised Outlier Detection via Multiple Thresholding](https://mlsanity.com/paper/2407.05382/) (2024)
- [MSD-LLM: Predicting Ship Detention in Port State Control Inspections with Large Language Model](https://mlsanity.com/paper/2505.19568/) (2025)
- [Unsupervised Feature Selection via Robust Autoencoder and Adaptive Graph Learning](https://mlsanity.com/paper/2512.18720/) (2025)

## Abstract (arXiv)

We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder maps the data into a latent space, from which the RSR layer extracts the subspace. The decoder then smoothly maps back the underlying subspace to a "manifold" close to the original inliers. Inliers and outliers are distinguished according to the distances between the original and mapped positions (small for inliers and large for outliers). Extensive numerical experiments with both image and document datasets demonstrate state-of-the-art precision and recall.