This article introduces a new system, OC1, for inducing oblique decision trees, which combines deterministic hill-climbing with randomization to find optimal oblique splits at each node. Oblique decision trees are particularly suited for numeric attributes, though they can be adapted for symbolic or mixed attributes. The authors present extensive empirical studies using real and artificial data to demonstrate that OC1 constructs smaller and more accurate trees compared to axis-parallel decision trees. The benefits of randomization in the construction of oblique decision trees are also examined. The paper discusses the challenges of inducing oblique decision trees, including computational complexity, and reviews existing methods such as CART with linear combinations, Linear Machine Decision Trees, and Simulated Annealing of Decision Trees. OC1 is designed to address these limitations by using a combination of deterministic hill-climbing and randomization techniques, ensuring efficient computation and avoiding local minima. The system is fully implemented and available online. Experiments show that OC1 outperforms other decision tree induction methods in various real-world domains, and randomization significantly improves the quality of the trees produced.This article introduces a new system, OC1, for inducing oblique decision trees, which combines deterministic hill-climbing with randomization to find optimal oblique splits at each node. Oblique decision trees are particularly suited for numeric attributes, though they can be adapted for symbolic or mixed attributes. The authors present extensive empirical studies using real and artificial data to demonstrate that OC1 constructs smaller and more accurate trees compared to axis-parallel decision trees. The benefits of randomization in the construction of oblique decision trees are also examined. The paper discusses the challenges of inducing oblique decision trees, including computational complexity, and reviews existing methods such as CART with linear combinations, Linear Machine Decision Trees, and Simulated Annealing of Decision Trees. OC1 is designed to address these limitations by using a combination of deterministic hill-climbing and randomization techniques, ensuring efficient computation and avoiding local minima. The system is fully implemented and available online. Experiments show that OC1 outperforms other decision tree induction methods in various real-world domains, and randomization significantly improves the quality of the trees produced.