# Revisiting Forest Proximities via Sparse Leaf-Incidence Kernels

arXiv: https://arxiv.org/abs/2601.02735 · HTML: https://mlsanity.com/paper/2601.02735/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 60 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 21 of 21)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Understanding Random Forests: From Theory to Practice](https://mlsanity.com/paper/1407.7502/) (2014)
- [The Tree Ensemble Layer: Differentiability meets Conditional Computation](https://mlsanity.com/paper/2002.07772/) (2020)
- [Geometry- and Accuracy-Preserving Random Forest Proximities](https://mlsanity.com/paper/2201.12682/) (2022)
- [The Random Forest Kernel and other kernels for big data from random partitions](https://mlsanity.com/paper/1402.4293/) (2014)
- [Learning with Asymmetric Kernels: Least Squares and Feature Interpretation](https://mlsanity.com/paper/2202.01397/) (2022)
- [A Novel Random Forest Dissimilarity Measure for Multi-View Learning](https://mlsanity.com/paper/2007.02572/) (2020)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [Explicating feature contribution using Random Forest proximity distances](https://mlsanity.com/paper/1807.06572/) (2018)
- [Making Sense of Random Forest Probabilities: a Kernel Perspective](https://mlsanity.com/paper/1812.05792/) (2018)
- [Supervised Manifold Learning via Random Forest Geometry-Preserving Proximities](https://mlsanity.com/paper/2307.01077/) (2023)
- [Enhanced Local Explainability and Trust Scores with Random Forest Proximities](https://mlsanity.com/paper/2310.12428/) (2023)
- [Learning in Feature Spaces via Coupled Covariances: Asymmetric Kernel SVD and Nystr"om method](https://mlsanity.com/paper/2406.08748/) (2024)
- [Forest Proximities for Time Series](https://mlsanity.com/paper/2410.03098/) (2024)
- [Random Forest-Supervised Manifold Alignment](https://mlsanity.com/paper/2411.15179/) (2024)
- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)
- [RFX: High-Performance Random Forests with GPU Acceleration and QLORA Compression](https://mlsanity.com/paper/2511.19493/) (2025)

## Built on by (most cited first, 1 of 1)

- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and restricts broader use in kernel and representation-learning pipelines. We introduce a unified view of leaf-collision forest proximities through a class of Separable Weighted Leaf-Collision (SWLC) kernels, showing that most existing proximities differ only in their weighting scheme while sharing a common sparse leaf-incidence structure. This yields an explicit leaf-space representation that clarifies their kernel interpretation and leads to an exact finite-sample sparse factorization of the proximity matrix, avoiding an explicit all-pairs comparison and reducing computation to sparse linear algebra over leaf collisions. We implement this framework in a memory-efficient Python library and show, both theoretically and empirically, that exact kernel computation scales near-linearly in time and memory under standard forest regimes. Benchmarks verify the predicted scaling behavior in practice across datasets, proximity definitions, and forest settings, and show that the resulting sparse leaf-space representation can also be used directly for fast task-aware embedding.