# k-NNN: Nearest Neighbors of Neighbors for Anomaly Detection

arXiv: https://arxiv.org/abs/2305.17695 · HTML: https://mlsanity.com/paper/2305.17695/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 28 May 2023.

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2010.05903/) (2020)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection](https://mlsanity.com/paper/2005.14140/) (2020)
- [Resnet in Resnet: Generalizing Residual Architectures](https://mlsanity.com/paper/1603.08029/) (2016)
- [Deep Nearest Neighbor Anomaly Detection](https://mlsanity.com/paper/2002.10445/) (2020)
- [Mean-Shifted Contrastive Loss for Anomaly Detection](https://mlsanity.com/paper/2106.03844/) (2021)
- [Anomaly Detection with Generative Adversarial Networks for Multivariate Time Series](https://mlsanity.com/paper/1809.04758/) (2018)
- [Statistical Analysis of Nearest Neighbor Methods for Anomaly Detection](https://mlsanity.com/paper/1907.03813/) (2019)
- [Latent space conditioning for improved classification and anomaly detection](https://mlsanity.com/paper/1911.10599/) (2019)

## Built on by (most cited first, 3 of 3)

- [Anomaly as Non-Conformity via Training-Free Graph Laplacian Energy Minimization](https://mlsanity.com/paper/2605.28428/) (2026)
- [Nearest-Neighbor Radii under Dependent Sampling](https://mlsanity.com/paper/2605.14343/) (2026)
- [Local Sparsity Enables Unsupervised LLM Safety Detection](https://mlsanity.com/paper/2609.20129/) (2026)

## Abstract (arXiv)

Anomaly detection aims at identifying images that deviate significantly from the norm. We focus on algorithms that embed the normal training examples in space and when given a test image, detect anomalies based on the features distance to the k-nearest training neighbors. We propose a new operator that takes into account the varying structure & importance of the features in the embedding space. Interestingly, this is done by taking into account not only the nearest neighbors, but also the neighbors of these neighbors (k-NNN). We show that by simply replacing the nearest neighbor component in existing algorithms by our k-NNN operator, while leaving the rest of the algorithms untouched, each algorithms own results are improved. This is the case both for common homogeneous datasets, such as flowers or nuts of a specific type, as well as for more diverse datasets