This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ion Trees (I) Waveform Example (CART) Three functions h1 ( ), h2 ( ), h3 ( ) are shifted versions of each other, as shown in the figure. Each hj is specified by the equallateral right triangle function. Its values at integers = 1 21 are measured. Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) The three classes of waveforms are random convex combinations of two of these waveforms plus independent Gaussian noise. Each sample is a 21 dimensional vector containing the values of the random waveforms measured at = 1, 2, ..., 21. To generate a sample in class 1, a random number u uniformly distributed in [0, 1] and 21 random numbers 1 , 2 , ..., 21 normally distributed with mean zero and variance 1 are generated. xj = uh1 (j) + (1  u)h2 (j) + j , j = 1, ..., 21. To generate a sample in class 2, repeat the above process to generate a random number u and 21 random numbers 1 , ..., 21 and set xj = uh1 (j) + (1  u)h3 (j) + j , Class 3 vectors are generated by xj = uh2 (j) + (1  u)h3 (j) + j , j = 1, ..., 21. j = 1, ..., 21. Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) Example random waveforms
6 Class 1 4 2 0 2 4 0 8 6 Class 2 4 2 0 2 0 6 4 Class 3 2 0 2 4 5 10 15 20 5 0 5 10 15 20 0 5 5 10 15 20 5 10 15 20 6 4 2 0 2 4 5 10 15 20 8 6 4 2 0 2 4 0 5 10 15 20 Jia Li http://www.stat.psu.edu/jiali Classification/Decision Trees (I) 300 random samples are generated using prior probabilities ( 1 , 1 , 1 ) for training. 3 3 3 Construction of the tree: The set of questions: {Is xj c?} for c ranging over all real numbers and j = 1, ..., 21. Gini index is used for measuring goodness of split. The final tree is...
View
Full
Document
This note was uploaded on 02/04/2012 for the course STAT 557 taught by Professor Jiali during the Fall '09 term at Penn State.
 Fall '09
 JIALI
 Statistics

Click to edit the document details