Hyperbolic space is becoming a popular choice for representing data due to
the hierarchical structure - whether implicit or explicit - of many real-world
datasets. Along with it comes a need for algorithms capable of solving
fundamental tasks, such as classification, in hyperbolic space. Recently,
multiple papers have investigated hyperbolic alternatives to hyperplane-based
classifiers, such as logistic regression and SVMs. While effective, these
approaches struggle with more complex hierarchical data. We, therefore, propose
to generalize the well-known random forests to hyperbolic space. We do this by
redefining the notion of a split using horospheres. Since finding the globally
optimal split is computationally intractable, we find candidate horospheres
through a large-margin classifier. To make hyperbolic random forests work on
multi-class data and imbalanced experiments, we furthermore outline a new
method for combining classes based on their lowest common ancestor and a
class-balanced version of the large-margin loss. Experiments on standard and
new benchmarks show that our approach outperforms both conventional random
forest algorithms and recent hyperbolic classifiers.

通过使用水平面将随机森林推广到双曲空间，使用大边际分类器找到候选分割，再结合子类最低共同祖先和类平衡的大边际损失方法，可以解决多类数据和不平衡实验问题，并且在标准和新的基准测试中表现优于传统随机森林算法和最近双曲分类器。