If you use 10-fold cross validation, which tree is representative?

If you use 10-fold cross validation to derive the error in, say, a C4.5 algorithm, then you are essentially building 10 separate trees on 90% of the data to test on 10% - 10 times. Which one of the 10 trees is representative? Won't they all be different?

For example - how does WEKA give me a C4.5 tree and a cross-validation error, but only one. I feel I must have fundamentally misunderstood this.

Thanks for any help

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Typically, you use the 10 cross-validated trees to estimate "out-of-sample" error, and then fit an 11th and final tree on the full dataset.

In theory, the error of the 11th tree on out-of-sample data should be similar to the out-of-sample error you estimated from the 10 cross-validated trees.

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Thanks. I am a moron. –  rosser Mar 5 '12 at 20:33
@rosser no worries! I had the same question the first time I used caret in R to cross validate a model. –  Zach Mar 5 '12 at 20:38