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Binary Decision Trees [2 P]

In a decision tree with only binary splits, an attribute may be selected more than once as splitting criterion. In this exercise you should construct a decision tree with only binary splits which classifies data according to two attributes $ X_1$ and $ X_2$ into two classes $ A$ and $ B$ . Figure 1 shows the connection between attributes and class membership:
Figure 1: Training data from classes A (green) and B (red).
\includegraphics[scale = 0.5]{traindata.eps}
Sketch the shape of a binary decision tree for this training set. Explain what leads to this shape.
What would you do to train a qualitatively better decision tree?

Pfeiffer Michael 2006-01-18