Each digit is represented by a 7 dimensional vector

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Unformatted text preview: ees (I) Digit 1 2 3 4 5 6 7 8 9 0 x1 0 1 1 0 1 1 1 1 1 1 x2 0 0 0 1 1 1 0 1 1 1 x3 1 1 1 1 0 0 1 1 1 1 x4 0 1 1 1 1 1 0 1 1 0 x5 0 1 0 0 0 1 0 1 0 1 x6 1 0 1 1 1 1 1 1 1 1 x7 0 1 1 0 1 1 0 1 1 1 Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) The data for the example are generated by a malfunctioning calculator. Each of the seven lights has probability 0.1 of being in the wrong state independently. The training set contains 200 samples generated according to the specified distribution. Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) A tree structured classifier is applied. The set of questions Q contains: Is xj = 0?, j = 1, 2, ..., 7. The twoing rule is used in splitting. The pruning cross-validation method is used to choose the right sized tree. Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) Classification performance: The error rate estimated by using a test set of size 5000 is 0.30. The error rate estimated by cross-validation using the training set is 0.30. The resubstitution estimate of the error rate is 0.29. The Bayes error rate is 0.26. There is little room for improvement over the tree classifier. Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) Accidently, every digit occupies one leaf node. In general, one class may occupy any number of leaf nodes and occasionally no leaf node. X6 and X7 are never used. Jia Li http://www.stat.psu.edu/jiali Classification/Decis...
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