Ensemble of Rotation Trees for Imbalanced Medical Datasets

Pseudocode 1

Pseudocode of ensemble of rotation trees for medical datasets.

Training:

Input:

   X_a—the abnormal set,

   X_n—the normal set,

   M—the number of classifiers in the ensemble

Output:

  the ensemble H with M classifiers

Begin:

1. ;

2. H =∅;

3. repeat

4. sample a subset D_n from ;

5. ; //balanced dataset

6. Split F into subsets: _,;

7. ;

8. repeat

9.  Let D_{i, j} be the data set of D_i for the feature in F_{i, j};

10.  Select a bootstrap sample subset D^’_{i, j} from D_{i, j} of size 50% of the number of objects in D_{i, j。} Denote as the new set;

11.  Apply PCA on F_{i, j} and D^’_{i, j} to obtain the coefficients in a matrix R_{i, j};

12. until j = n/L

13. Arrange the R_{i, j} in a rotation matrix R_i as in equation (1), ; //refer to (1)

14. D_{i, train} = D_iR_i; //obtain novel dataset through projecting balanced dataset D_i to the new space defined by R_i

15. Build classifier h_i using D_{i, train}; //learn classifier on the novel balanced dataset D_i

16. ;

17. until i = M

18. return H

Classification Phase:

For a given x, let h_i(R_ix) be the probability assigned by the classifier h_i to the hypothesis that x comes from class ω_j. Calculate the confidence for each class that x belongs to using the average combination method:

Assign x to the class with the largest confidence.