# Geometry- and Accuracy-Preserving Random Forest Proximities

arXiv: https://arxiv.org/abs/2201.12682 · HTML: https://mlsanity.com/paper/2201.12682/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 63 references that are in the map.
- First posted on arXiv 29 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [To tune or not to tune the number of trees in random forest?](https://mlsanity.com/paper/1705.05654/) (2017)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [The Random Forest Kernel and other kernels for big data from random partitions](https://mlsanity.com/paper/1402.4293/) (2014)
- [A Novel Random Forest Dissimilarity Measure for Multi-View Learning](https://mlsanity.com/paper/2007.02572/) (2020)
- [Explicating feature contribution using Random Forest proximity distances](https://mlsanity.com/paper/1807.06572/) (2018)
- [Visualizing High Dimensional Dynamical Processes](https://mlsanity.com/paper/1906.10725/) (2019)

## Built on by (most cited first, 24 of 24)

- [Quantifying Outlierness of Funds from their Categories using Supervised Similarity](https://mlsanity.com/paper/2308.06882/) (2023)
- [EMBERSim: A Large-Scale Databank for Boosting Similarity Search in Malware Analysis](https://mlsanity.com/paper/2310.01835/) (2023)
- [Open Set Recognition for Random Forest](https://mlsanity.com/paper/2408.02684/) (2024)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [Supervised Manifold Learning via Random Forest Geometry-Preserving Proximities](https://mlsanity.com/paper/2307.01077/) (2023)
- [Forest Proximities for Time Series](https://mlsanity.com/paper/2410.03098/) (2024)
- [Quantile Regression using Random Forest Proximities](https://mlsanity.com/paper/2408.02355/) (2024)
- [Can an unsupervised clustering algorithm reproduce a categorization system?](https://mlsanity.com/paper/2408.10340/) (2024)
- [Enhancing Supervised Visualization through Autoencoder and Random Forest Proximities for Out-of-Sample Extension](https://mlsanity.com/paper/2406.04421/) (2024)
- [Case-based Explainability for Random Forest: Prototypes, Critics, Counter-factuals and Semi-factuals](https://mlsanity.com/paper/2408.06679/) (2024)
- [Explainable Unsupervised Anomaly Detection with Random Forest](https://mlsanity.com/paper/2504.16075/) (2025)
- [Surrogate Interpretable Graph for Random Decision Forests](https://mlsanity.com/paper/2506.01988/) (2025)
- [Label-Guided Imputation via Forest-Based Proximities for Improved Time Series Classification](https://mlsanity.com/paper/2509.22919/) (2025)
- [Revisiting Forest Proximities via Sparse Leaf-Incidence Kernels](https://mlsanity.com/paper/2601.02735/) (2026)
- [Machine Learning Models for Accurately Predicting Properties of CsPbCl3 Perovskite Quantum Dots](https://mlsanity.com/paper/2406.15515/) (2024)
- [Detecting and explaining clinical-omics inconsistencies to improve patient cohort stratification: an application to Parkinson's disease](https://mlsanity.com/paper/2507.03656/) (2025)
- [Localized Uncertainty Quantification in Random Forests via Proximities](https://mlsanity.com/paper/2509.22928/) (2025)
- [Interpretable Model-Aware Counterfactual Explanations for Random Forest](https://mlsanity.com/paper/2510.27397/) (2025)
- [The Generalized Proximity Forest](https://mlsanity.com/paper/2511.19487/) (2025)
- [Freeze, Diffuse, Decode: Task-Aware Adaptation of Transformer Embeddings for Antimicrobial Peptide Design](https://mlsanity.com/paper/2511.23120/) (2025)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)
- [A Unified Evaluation of Learning-Based Similarity Techniques for Malware Detection](https://mlsanity.com/paper/2602.15376/) (2026)
- [Kernel of Partition Paths: A Unified Representation for Tree Ensembles](https://mlsanity.com/paper/2606.18853/) (2026)
- [What Makes a Peer? Valuation-Anchored Similarity in Private Markets](https://mlsanity.com/paper/2608.12594/) (2026)

## Abstract (arXiv)

Random forests are considered one of the best out-of-the-box classification and regression algorithms due to their high level of predictive performance with relatively little tuning. Pairwise proximities can be computed from a trained random forest and measure the similarity between data points relative to the supervised task. Random forest proximities have been used in many applications including the identification of variable importance, data imputation, outlier detection, and data visualization. However, existing definitions of random forest proximities do not accurately reflect the data geometry learned by the random forest. In this paper, we introduce a novel definition of random forest proximities called Random Forest-Geometry- and Accuracy-Preserving proximities (RF-GAP). We prove that the proximity-weighted sum (regression) or majority vote (classification) using RF-GAP exactly matches the out-of-bag random forest prediction, thus capturing the data geometry learned by the random forest. We empirically show that this improved geometric representation outperforms traditional random forest proximities in tasks such as data imputation and provides outlier detection and visualization results consistent with the learned data geometry.