Figure 4.

Illustration of space partition and random projection trees. The superscripts indicate the order of tree node split. One starts with the root node, ${\mathcal{D}}^{(0)}$, which corresponds to all the data. After the first split, ${\mathcal{D}}^{(0)}$ is partitioned into its two child nodes, {${\mathcal{D}}_L^{(1)}$, ${\mathcal{D}}_R^{(1)}$}. The second split partitions the left child node, ${\mathcal{D}}_L^{(1)}$, into its two child nodes, {${\mathcal{D}}_L^{(2)}$, ${\mathcal{D}}_R^{(2)}$}. The third split, which split the right child node of the root node, ${\mathcal{D}}_R^{(1)}$, leads to two new child nodes, {${\mathcal{D}}_L^{(3)}$, ${\mathcal{D}}_R^{(3)}$}. This process continues until a stopping criterion is met.