# Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation

arXiv: https://arxiv.org/abs/2105.14737 · HTML: https://mlsanity.com/paper/2105.14737/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 20 of 20)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Future Frame Prediction for Anomaly Detection -- A New Baseline](https://mlsanity.com/paper/1712.09867/) (2017)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2006.16067/) (2020)
- [Latent Space Autoregression for Novelty Detection](https://mlsanity.com/paper/1807.01653/) (2018)
- [Segmentation-Based Deep-Learning Approach for Surface-Defect Detection](https://mlsanity.com/paper/1903.08536/) (2019)
- [Explainable Deep One-Class Classification](https://mlsanity.com/paper/2007.01760/) (2020)
- [Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection](https://mlsanity.com/paper/2005.14140/) (2020)
- [Mixed supervision for surface-defect detection: from weakly to fully supervised learning](https://mlsanity.com/paper/2104.06064/) (2021)
- [The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings](https://mlsanity.com/paper/1703.00864/) (2017)
- [OL'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning](https://mlsanity.com/paper/1712.01727/) (2017)
- [One-Class Classification: A Survey](https://mlsanity.com/paper/2101.03064/) (2021)

## Built on by (most cited first, 26 of 26)

- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [Generative Cooperative Learning for Unsupervised Video Anomaly Detection](https://mlsanity.com/paper/2203.03962/) (2022)
- [Deep Learning for Unsupervised Anomaly Localization in Industrial Images: A Survey](https://mlsanity.com/paper/2207.10298/) (2022)
- [IM-IAD: Industrial Image Anomaly Detection Benchmark in Manufacturing](https://mlsanity.com/paper/2301.13359/) (2023)
- [Prototypical Residual Networks for Anomaly Detection and Localization](https://mlsanity.com/paper/2212.02031/) (2022)
- [Mutual Information Divergence: A Unified Metric for Multimodal Generative Models](https://mlsanity.com/paper/2205.13445/) (2022)
- [Exploring Diffusion Models for Unsupervised Video Anomaly Detection](https://mlsanity.com/paper/2304.05841/) (2023)
- [A Survey on Unsupervised Anomaly Detection Algorithms for Industrial Images](https://mlsanity.com/paper/2204.11161/) (2022)
- [Unsupervised Video Anomaly Detection with Diffusion Models Conditioned on Compact Motion Representations](https://mlsanity.com/paper/2307.01533/) (2023)
- [U-Flow: A U-shaped Normalizing Flow for Anomaly Detection with Unsupervised Threshold](https://mlsanity.com/paper/2211.12353/) (2022)
- [LafitE: Latent Diffusion Model with Feature Editing for Unsupervised Multi-class Anomaly Detection](https://mlsanity.com/paper/2307.08059/) (2023)
- [A Coarse-to-Fine Pseudo-Labeling (C2FPL) Framework for Unsupervised Video Anomaly Detection](https://mlsanity.com/paper/2310.17650/) (2023)
- [What makes a good data augmentation for few-shot unsupervised image anomaly detection?](https://mlsanity.com/paper/2304.03294/) (2023)
- [Few-Shot Anomaly Detection via Category-Agnostic Registration Learning](https://mlsanity.com/paper/2406.08810/) (2024)
- [ADPS: Asymmetric Distillation Post-Segmentation for Image Anomaly Detection](https://mlsanity.com/paper/2210.10495/) (2022)
- [Efficient Non-Compression Auto-Encoder for Driving Noise-based Road Surface Anomaly Detection](https://mlsanity.com/paper/2111.10985/) (2021)
- [IPAD: Industrial Process Anomaly Detection Dataset](https://mlsanity.com/paper/2404.15033/) (2024)
- [ONER: Online Experience Replay for Incremental Anomaly Detection](https://mlsanity.com/paper/2412.03907/) (2024)
- [Weakly supervised marine animal detection from remote sensing images using vector-quantized variational autoencoder](https://mlsanity.com/paper/2307.06720/) (2023)
- [A Recover-then-Discriminate Framework for Robust Anomaly Detection](https://mlsanity.com/paper/2406.04608/) (2024)
- [Dual-Branch Reconstruction Network for Industrial Anomaly Detection with RGB-D Data](https://mlsanity.com/paper/2311.06797/) (2023)
- [TeG: Temporal-Granularity Method for Anomaly Detection with Attention in Smart City Surveillance](https://mlsanity.com/paper/2411.11003/) (2024)
- [[Reproducibility Report] Explainable Deep One-Class Classification](https://mlsanity.com/paper/2206.02598/) (2022)
- [Anomaly segmentation model for defects detection in electroluminescence images of heterojunction solar cells](https://mlsanity.com/paper/2208.05994/) (2022)
- [Gaussian Image Anomaly Detection with Greedy Eigencomponent Selection](https://mlsanity.com/paper/2308.04944/) (2023)
- [RobustA: Robust Anomaly Detection in Multimodal Data](https://mlsanity.com/paper/2511.07276/) (2025)

## Abstract (arXiv)

We present the efficiency of semi-orthogonal embedding for unsupervised anomaly segmentation. The multi-scale features from pre-trained CNNs are recently used for the localized Mahalanobis distances with significant performance. However, the increased feature size is problematic to scale up to the bigger CNNs, since it requires the batch-inverse of multi-dimensional covariance tensor. Here, we generalize an ad-hoc method, random feature selection, into semi-orthogonal embedding for robust approximation, cubically reducing the computational cost for the inverse of multi-dimensional covariance tensor. With the scrutiny of ablation studies, the proposed method achieves a new state-of-the-art with significant margins for the MVTec AD, KolektorSDD, KolektorSDD2, and mSTC datasets. The theoretical and empirical analyses offer insights and verification of our straightforward yet cost-effective approach.