Binary recursive partitioning

To keep the description of the regions simple, binary decision trees with a root, nodes, and leaves, the R, s, are favored. Each region is split into two further regions over and over again termed a recursive binary partitioning. The decision for the binary split is based on a constant, s, as shown in Figure 5.34b. 

Figure 5.34 Partitioning in CART The panel (a) demonstrates the partitioning of a two-dimensional feature space into four regions by recursive binary splitting. In the panel (b), the resulting tree is shown.

Is this a valid partitioning of regions emerging from a recursive binary splitting ... 

Another nonparametric regression method is CART (classification and regression trees). The basic concepts were outlined in Discriminant Analysis Section about tree-based classification. We remember from that chapter that CART is a recursive binary partition method based on a simple model constant for each region. If the residual sums of squares of responses is minimized. 

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