result of rpart is a root, but data shows Information Gain

Understanding the Discrepancy

Rpart’s Root Node

The root node in a recursive partitioning (rpart) decision tree is the initial node that encompasses all data points. This node represents the starting point of the decision-making process.

Information Gain

Information gain, on the other hand, measures the reduction in uncertainty achieved by splitting a node into its child nodes. It is calculated based on the distribution of target classes within a node.

The Root Node vs. Information Gain

Root Node as Starting Point

The root node, being the starting point of the rpart process, does not inherently possess information gain. It represents the initial state of the data before any splitting occurs.

Information Gain as a Splitting Criterion

Information gain is used as a criterion for selecting the best split at each node. It determines which variable and threshold will result in the most significant reduction in uncertainty about the target variable.

Example Scenario

Data:

Rpart Output:

  Node number: 1
  Split: Income < 55000
  Left child: 2
  Right child: 3

  Node number: 2
  Split: Age < 32.5
  Left child: 4
  Right child: 5

Information Gain:

The initial root node (Node 1) has no information gain because no splitting has occurred yet. The subsequent splits, however, demonstrate information gain:

• Splitting on Income at Node 1 results in a decrease in uncertainty about whether a customer will purchase (Yes/No).
• Splitting on Age at Node 2 further reduces uncertainty based on the age distribution in the child nodes.

Conclusion

In essence, the rpart root node is simply the starting point for the decision tree, and information gain is used as a criterion to guide the splitting process. While the root node itself does not possess information gain, the subsequent splits in the tree reflect the reduction in uncertainty as a result of the information gain achieved at each level.