将超球决策树改造为可直接使用欧式树模型的封装，提速并简化代码。
Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach
- 用贝尔特拉米-克莱因模型重写超球决策树，保留阈值划分机制。
- 通过前后处理封装，使原有欧式树模型无需修改即可加速运行。
- 适合需要高效超球学习且想复用现有代码的开发者使用。
决策树及其衍生模型在欧氏空间中是机器学习的基石。近期工作将这些模型扩展到洛伦茨模型的双曲空间，通过用齐次超平面替代轴对齐超平面来分割输入空间。本文展示如何将超球决策树（hyperDT）算法优雅地重表达为贝尔特拉米-克莱因模型中的形式。该方法保持了欧氏决策树中使用的阈值操作，使得hyperDT可被重写为针对设计用于欧氏空间的树模型的简单预处理和后处理步骤，形成一个封装。此封装解锁了欧氏空间模型中已有的多种优化，提升了灵活性、速度与精度，同时提供更简洁、可维护和可扩展的代码库。实现代码已开源：https://github.com/pchlenski/hyperdt。
原文摘要 · Abstract (English)
Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with homogeneous hyperplanes when partitioning the input space. In this paper, we show how the hyperDT algorithm can be elegantly reexpressed in the Beltrami-Klein model of hyperbolic spaces. This preserves the thresholding operation used in Euclidean decision trees, enabling us to further rewrite hyperDT as simple pre- and post-processing steps that form a wrapper around existing tree-based models designed for Euclidean spaces. The wrapper approach unlocks many optimizations already available in Euclidean space models, improving flexibility, speed, and accuracy while offering a simpler, more maintainable, and extensible codebase. Our implementation is available at https://github.com/pchlenski/hyperdt.
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