Final answer:
A decision tree algorithm decides on the variable to split at each node based on measures of impurity, such as Gini impurity, and recursively applies this process to create a tree that classifies the data.
Step-by-step explanation:
A decision tree algorithm decides on which variable to split at the root node and its succeeding child nodes based on certain criteria. One common criterion is Gini impurity, which measures the probability of misclassifying a randomly chosen element. The algorithm calculates the impurity of each variable and selects the variable that results in the greatest reduction in impurity when split. This process is repeated recursively for each child node until a stopping criterion is met.
For example, let's say we have a dataset with two variables: age and income, and the goal is to predict whether a person will buy a product or not. The algorithm might initially split the data based on age, as it determines that age is the most informative variable. The tree will then branch out based on different age ranges, and for each branch, it will further split the data based on another variable, such as income. This process continues until the stopping criterion is met, such as a maximum depth or minimum number of samples in a node.
In summary, a decision tree algorithm decides on the variable to split at each node based on measures of impurity, such as Gini impurity, and recursively applies this process to create a tree that classifies the data.