# K-nearest Neighbor Search by Random Projection Forests

arXiv: https://arxiv.org/abs/1812.11689 · HTML: https://mlsanity.com/paper/1812.11689/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2018.

## Built on by (most cited first, 10 of 10)

- [Medical Image Retrieval via Nearest Neighbor Search on Pre-trained Image Features](https://mlsanity.com/paper/2210.02401/) (2022)
- [Chameleon2++: An Efficient and Scalable Variant Of Chameleon Clustering](https://mlsanity.com/paper/2501.02612/) (2025)
- [A Computational Approach to Improving Fairness in K-means Clustering](https://mlsanity.com/paper/2505.22984/) (2025)
- [Graph Construction using Principal Axis Trees for Simple Graph Convolution](https://mlsanity.com/paper/2302.12000/) (2023)
- [Random Projection Forest Initialization for Graph Convolutional Networks](https://mlsanity.com/paper/2302.12001/) (2023)
- [The Effect of Points Dispersion on the k-nn Search in Random Projection Forests](https://mlsanity.com/paper/2302.13160/) (2023)
- [Random projection tree similarity metric for SpectralNet](https://mlsanity.com/paper/2302.13168/) (2023)
- [CBR -- Boosting Adaptive Classification By Retrieval of Encrypted Network Traffic with Out-of-distribution](https://mlsanity.com/paper/2403.11206/) (2024)
- [ANN Search: Recall What Matters](https://mlsanity.com/paper/2606.04522/) (2026)
- [Mitigating Visual Hallucinations in Multimodal Systems through Retrieval-Augmented Reliability-Aware Inference](https://mlsanity.com/paper/2606.15782/) (2026)

## Abstract (arXiv)

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we propose random projection forests (rpForests), for kNN search. rpForests finds kNNs by aggregating results from an ensemble of random projection trees with each constructed recursively through a series of carefully chosen random projections. rpForests achieves a remarkable accuracy in terms of fast decay in the missing rate of kNNs and that of discrepancy in the kNN distances. rpForests has a very low computational complexity. The ensemble nature of rpForests makes it easily run in parallel on multicore or clustered computers; the running time is expected to be nearly inversely proportional to the number of cores or machines. We give theoretical insights by showing the exponential decay of the probability that neighboring points would be separated by ensemble random projection trees when the ensemble size increases. Our theory can be used to refine the choice of random projections in the growth of trees, and experiments show that the effect is remarkable.