| Corral : correlated attribute.  By Ronny Kohavi
| First used in John, Kohavi, and Pfleger, 
|    Irrelevant features and the subset selection
|    problem. In Machine Learning: Proceedings of the Eleventh International
|    Conference, 1994, available in http://robotics.stanford.edu/~ronnyk
|
| Basic idea: This is an artificial domain where the target concept is 
|     (A0^A1) V (B0^B1)
| Irr is irrelevant, and Correlated is an attribute highly correlated with 
|   the label, but with 25% error rate.  The training set was selected
|   manually to make it hard for decision trees to deal with this problem.
| All decision tree algorithms I tested (ID3, Cart, C4.5) pick the
|   "Correlated" attribute as the root split.  This is the worst decision
|   possible because the data splits into two and to get 100%, the problem
|   must be solved again for each subtree.
| Feature subset selection solves the problem because it hides this attribute
|   from the decison tree algorithm.
| C4.5AP (automatic parameter selection for C4.5 provided by MLC++) 
|   discovered a set of parameters for C4.5 (-m1 -c80) which causes
|   C4.5 to prune up, replacing the root node with its left subtree which
|   is correct, thus getting 100% accuracy.  Note however that this
|   is a postprocessing step, and the original tree still contains the
|   correlated attribute at the root.
| 
| The idea for the test set is to have 25% noise in the last bit (correlated).
| Hence each instance for A, B, C, D, IRR repeats 4 times
| (hence 32*4) and one of them has the Corr bit wrong.
| For example, let's look at 0,0,0,0 for A,B,C,D
| 
| 0, 0, 0, 0, 0, 0, 0.
| 0, 0, 0, 0, 0, 0, 0.
| 0, 0, 0, 0, 0, 0, 0.
| 0, 0, 0, 0, 0, 1, 0.
| 
| 0, 0, 0, 0, 1, 0, 0.
| 0, 0, 0, 0, 1, 0, 0.
| 0, 0, 0, 0, 1, 0, 0.
| 0, 0, 0, 0, 1, 1, 0.



1,0

A0: 0,1
A1: 0,1
B0: 0,1
B1: 0,1
Irrelevant: 0,1
Correlated:0,1