Classification and Regression Trees

For all 642592 possible features a Classification and Regression Tree (CART) is created. CART analysis is a form of binary recursive partitioning. Each node is split into two child nodes, the original node is called a parent node. The term ``recursive'' refers to the fact that the binary partitioning process is applied over and over to reach a given number of splits (i.e., 6 splits in the case of the object volksbot). In order to find the best possible split features, we compute all possible splits, as well as all possible return values to be used in a split node. The program seeks to maximize the average ``purity'' of the two child nodes using the misclassification error measure [17]. Fig. (left) shows a simple feature classifier and a simple CART (right).

Figure: Left: A simple feature classifier with its threshold and return values $\alpha$ and $\beta$. Right: A Classification and Regression Tree with 4 splits. According to the specific filter applied to the image input section $x$, the output of the tree, $h(x)$ is calculated, depending on the threshold values.