# Canonical Correlation Forests

arXiv: https://arxiv.org/abs/1507.05444 · HTML: https://mlsanity.com/paper/1507.05444/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2015.

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

- [Minimax Rates for High-Dimensional Random Tessellation Forests](https://mlsanity.com/paper/2109.10541/) (2021)
- [Accelerated and interpretable oblique random survival forests](https://mlsanity.com/paper/2208.01129/) (2022)
- [Decision-forest voting scheme for classification of rare classes in network intrusion detection](https://mlsanity.com/paper/2107.11862/) (2021)
- [Mapping Slums with Medium Resolution Satellite Imagery: a Comparative Analysis of Multi-Spectral Data and Grey-level Co-occurrence Matrix Techniques](https://mlsanity.com/paper/2106.11395/) (2021)
- [Shape Modeling with Spline Partitions](https://mlsanity.com/paper/2108.02507/) (2021)
- [Hyperspectral Image Analysis in Single-Modal and Multimodal setting using Deep Learning Techniques](https://mlsanity.com/paper/2403.01546/) (2024)
- [Statistical Advantages of Oblique Randomized Decision Trees and Forests](https://mlsanity.com/paper/2407.02458/) (2024)
- [Heterogeneous Random Forest](https://mlsanity.com/paper/2410.19022/) (2024)
- [Oblique Bayesian additive regression trees](https://mlsanity.com/paper/2411.08849/) (2024)
- [Jacobian Aligned Random Forests](https://mlsanity.com/paper/2512.08306/) (2025)
- [Vectorized Dynamic Histograms for Sparse Oblique Forests](https://mlsanity.com/paper/2603.00326/) (2026)
- [TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees](https://mlsanity.com/paper/2607.27027/) (2026)

## Abstract (arXiv)

We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives, the decision surfaces of CCFs are not restricted to the coordinate system of the inputs features and therefore more naturally represent data with correlated inputs. CCFs naturally accommodate multiple outputs, provide a similar computational complexity to random forests, and inherit their impressive robustness to the choice of input parameters. As part of the CCF training algorithm, we also introduce projection bootstrapping, a novel alternative to bagging for oblique decision tree ensembles which maintains use of the full dataset in selecting split points, often leading to improvements in predictive accuracy. Our experiments show that, even without parameter tuning, CCFs out-perform axis-aligned random forests and other state-of-the-art tree ensemble methods on both classification and regression problems, delivering both improved predictive accuracy and faster training times. We further show that they outperform all of the 179 classifiers considered in a recent extensive survey.