Partitioning trees are efficient data structures for $k$-nearest neighbor
search. Machine learning libraries commonly use a special type of partitioning
trees called $k$d-trees to perform $k$-nn search. Unfortunately, $k$d-trees can
be ineffective in high dimensions because they need more tree levels to
decrease the vector quantization (VQ) error. Random projection trees rpTrees
solve this scalability problem by using random directions to split the data. A
collection of rpTrees is called rpForest. $k$-nn search in an rpForest is
influenced by two factors: 1) the dispersion of points along the random
direction and 2) the number of rpTrees in the rpForest. In this study, we
investigate how these two factors affect the $k$-nn search with varying $k$
values and different datasets. We found that with larger number of trees, the
dispersion of points has a very limited effect on the $k$-nn search. One should
use the original rpTree algorithm by picking a random direction regardless of
the dispersion of points.

本文探讨了两种影响随机投影森林中 k - 最近邻搜索 (K-NN 搜索) 性能的因素（数据点的分散性和 rpForest 中树的数量），研究表明随机投影森林的数量较大时，数据点的分散性对 K-NN 搜索影响非常有限。因此，在选择随机方向时，应使用原始 rpTree 算法，而不考虑数据点的分散性。