# CO2 Forest: Improved Random Forest by Continuous Optimization of Oblique Splits

arXiv: https://arxiv.org/abs/1506.06155 · HTML: https://mlsanity.com/paper/1506.06155/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2015.

## Built on by (most cited first, 4 of 4)

- [LHT: Statistically-Driven Oblique Decision Trees for Interpretable Classification](https://mlsanity.com/paper/2505.04139/) (2025)
- [OF-AE: Oblique Forest AutoEncoders](https://mlsanity.com/paper/2301.00880/) (2023)
- [Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach](https://mlsanity.com/paper/2506.04360/) (2025)
- [Discovery of fully efficient fault indicators along a data-based diagnosis process](https://mlsanity.com/paper/2609.28087/) (2026)

## Abstract (arXiv)

We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search to find good univariate split functions. In contrast, our method computes a linear combination of the features at each node, and optimizes the parameters of the linear combination (oblique) split functions by adopting a variant of latent variable SVM formulation. We develop a convex-concave upper bound on the classification loss for a one-level decision tree, and optimize the bound by stochastic gradient descent at each internal node of the tree. Forests of up to 1000 Continuously Optimized Oblique (CO2) decision trees are created, which significantly outperform Random Forest with univariate splits and previous techniques for constructing oblique trees. Experimental results are reported on multi-class classification benchmarks and on Labeled Faces in the Wild (LFW) dataset.