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。

随机投影森林中点分布对 k-nn 搜索的影响

The Effect of Points Dispersion on the $k$-nn Search in Random Projection Forests

Graph convolutional networks (GCNs) were a great step towards extending deep
learning to unstructured data such as graphs. But GCNs still need a constructed
graph to work with. To solve this problem, classical graphs such as $k$-nearest
neighbor are usually used to initialize the GCN. Although it is computationally
efficient to construct $k$-nn graphs, the constructed graph might not be very
useful for learning. In a $k$-nn graph, points are restricted to have a fixed
number of edges, and all edges in the graph have equal weights. We present a
new way to construct the graph and initialize the GCN. It is based on random
projection forest (rpForest). rpForest enables us to assign varying weights on
edges indicating varying importance, which enhanced the learning. The number of
trees is a hyperparameter in rpForest. We performed spectral analysis to help
us setting this parameter in the right range. In the experiments, initializing
the GCN using rpForest provides better results compared to $k$-nn
initialization.

本文介绍了一种新的构建图形和初始化 GCN 的方法，基于 rpForest，并通过谱分析来设置该参数的正确范围，实验结果表明，使用 rpForest 初始化 GCN 比 $k$-nn 初始化方法提供更好的结果。