  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.
