# AnomalyHop: An SSL-based Image Anomaly Localization Method

arXiv: https://arxiv.org/abs/2105.03797 · HTML: https://mlsanity.com/paper/2105.03797/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 8 May 2021.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2006.16067/) (2020)
- [Explainable Deep One-Class Classification](https://mlsanity.com/paper/2007.01760/) (2020)
- [DFR: Deep Feature Reconstruction for Unsupervised Anomaly Segmentation](https://mlsanity.com/paper/2012.07122/) (2020)
- [Interpretable Convolutional Neural Networks via Feedforward Design](https://mlsanity.com/paper/1810.02786/) (2018)
- [Iterative energy-based projection on a normal data manifold for anomaly localization](https://mlsanity.com/paper/2002.03734/) (2020)
- [PointHop: An Explainable Machine Learning Method for Point Cloud Classification](https://mlsanity.com/paper/1907.12766/) (2019)
- [PixelHop++: A Small Successive-Subspace-Learning-Based (SSL-based) Model for Image Classification](https://mlsanity.com/paper/2002.03141/) (2020)
- [Understanding Convolutional Neural Networks with A Mathematical Model](https://mlsanity.com/paper/1609.04112/) (2016)
- [Subspace Support Vector Data Description](https://mlsanity.com/paper/1802.03989/) (2018)
- [DefakeHop: A Light-Weight High-Performance Deepfake Detector](https://mlsanity.com/paper/2103.06929/) (2021)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [PointHop++: A Lightweight Learning Model on Point Sets for 3D Classification](https://mlsanity.com/paper/2002.03281/) (2020)
- [VoxelHop: Successive Subspace Learning for ALS Disease Classification Using Structural MRI](https://mlsanity.com/paper/2101.05131/) (2021)
- [Unsupervised Feedforward Feature (UFF) Learning for Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2009.01280/) (2020)
- [FaceHop: A Light-Weight Low-Resolution Face Gender Classification Method](https://mlsanity.com/paper/2007.09510/) (2020)
- [Multimodal Subspace Support Vector Data Description](https://mlsanity.com/paper/1904.07698/) (2019)
- [NITES: A Non-Parametric Interpretable Texture Synthesis Method](https://mlsanity.com/paper/2009.01376/) (2020)
- [Successive Subspace Learning: An Overview](https://mlsanity.com/paper/2103.00121/) (2021)
- [Low-Resolution Face Recognition In Resource-Constrained Environments](https://mlsanity.com/paper/2011.11674/) (2020)
- [An Interpretable Compression and Classification System: Theory and Applications](https://mlsanity.com/paper/1907.08952/) (2019)
- [Noise-Aware Texture-Preserving Low-Light Enhancement](https://mlsanity.com/paper/2009.01385/) (2020)
- [Dynamic Texture Synthesis by Incorporating Long-range Spatial and Temporal Correlations](https://mlsanity.com/paper/2104.05940/) (2021)

## Built on by (most cited first, 12 of 12)

- [PEDENet: Image Anomaly Localization via Patch Embedding and Density Estimation](https://mlsanity.com/paper/2110.15525/) (2021)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [DefakeHop++: An Enhanced Lightweight Deepfake Detector](https://mlsanity.com/paper/2205.00211/) (2022)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Green Steganalyzer: A Green Learning Approach to Image Steganalysis](https://mlsanity.com/paper/2306.04008/) (2023)
- [A Tiny Machine Learning Model for Point Cloud Object Classification](https://mlsanity.com/paper/2303.10898/) (2023)

## Abstract (arXiv)

An image anomaly localization method based on the successive subspace learning (SSL) framework, called AnomalyHop, is proposed in this work. AnomalyHop consists of three modules: 1) feature extraction via successive subspace learning (SSL), 2) normality feature distributions modeling via Gaussian models, and 3) anomaly map generation and fusion. Comparing with state-of-the-art image anomaly localization methods based on deep neural networks (DNNs), AnomalyHop is mathematically transparent, easy to train, and fast in its inference speed. Besides, its area under the ROC curve (ROC-AUC) performance on the MVTec AD dataset is 95.9%, which is among the best of several benchmarking methods. Our codes are publicly available at Github.