# Decision Trees

### Introduction

It is natural and intuitive to classify a pattern through a sequence of questions, in which the next question asked depends on the answer to the current question. This *20-questions* approach is particularly useful for nonmetric data, because all of the questions can be asked in *yes/no* or *true/false* or *value(property)∈ set of values* style that does not require any notion of metric.

### Theory

Such a sequence of questions is displayed in a directed * decision tree* or simply *tree*, where by convention the first or *root node* is displayed at the top, connected by successive (directional) *links* or *branches* to other nodes. These are similarly connected until we reach the terminal or *leaf* nodes, which have no further links.

#### Classification of Trees

The classification of a particular pattern begins at the root node, which asks for the value of a particular property of the pattern. The different links from from different root nodes correspond to the different possible values. Based on the answer we follow the link to the subsequent or *descendent* node. The next step is to make the decision at the appropriate subsequent node, which can be considered the root of a *subtree*. We continue this way until we reach a leaf node, which has no further questions. Each leaf node bears a category label and the test pattern is assigned the category of the leaf node reached.

## R-CARET

Decison Trees can be implemented in CARET using the following methods :

- Recursive Partitioning
- Boosted Trees
- Random Forests
- Other Trees(Node Harvest)