Decision Tree (ID3)
Interactive lab
Try it: Decision Tree (ID3)
How ID3 grows a decision tree greedily: label the node by majority vote, compute the gain of every remaining attribute, split on the best one, and recurse until the node is pure or no attributes are left — then classify a new row by walking the tree.
How it works
- Start with one root leaf holding every row and give it the majority label.
- If all rows agree, or no attributes are left, the node stays a leaf.
- Otherwise compute Gain(S, i) = C(S) - sum over values v of |S_v|/|S| · C(S_v) for each remaining attribute (C = entropy, training error or Gini).
- Split on the attribute with the largest gain and repeat on every child with that attribute removed.
- Classify a query by following its attribute values from the root to a leaf.
Default run (15 steps): ID3 starts with one root leaf holding all 14 rows (9 Yes / 5 No); its majority label is Yes. Impurity measure: entropy. … The query reaches the leaf Humidity = Normal: prediction Play = Yes.
Simplified: A fixed 4-attribute categorical table (at most 14 rows) with a Yes/No label. A value with no rows becomes a leaf with the parent's majority label, and a tied majority keeps the parent's label; real trees also prune.
Educational simulation
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