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This section proposes a novel Rotation Forest called Embedding Undersampling Rotation Forest (EURF) to handle class-imbalance problem.
As shown in Figure 1, EURF first splits the original training set (X, Y) into two disjoint sets based on the class labels, namely, majority class set ([X.sub.maj], [Y.sub.maj]) and minority class set ([X.sub.maj], [Y.sub.maj]).
After the learning rotation matrix R, EURF learns a classifier h on balanced data (X', Y') in the rotation feature space defined by R, namely, learning h from (X'R, Y'), where (X', Y') is obtained by merging minority class set ([X.sub.min], [Y.sub.min]) and undersampled subset ([X'.sub.maj], [Y.sub.maj]) of the majority class set and [absolute value of [X.sub.min]] = [absolute value of [X'.sub.maj]].
Algorithm 4 shows the pseudocode for EURF. The differences with Rotation Forest (refers to Algorithm 3) are mainly shown in lines 4~5 and lines 14~15.
The accuracy of EURF (the proposed method) on the minority class is guaranteed by the undersampling technique through the following two approaches: (1) undersampling the majority class to construct balanced data sets on which individual classifiers are constructed, forcing the learned classifiers to focus more on the minority class (lines 14-16, Algorithm 4) and (2) re-undersample the majority class to construct balanced data sets for training rotation matrices, and thus the matrices capture more information from the minority class, enhancing the accuracy of individual classifiers on the minority class (lines 7~11, Algorithm 4).
Diversity is a key to the success of an ensemble, and the diversity of EURF mainly comes from the learning process of both rotation matrices and individual classifier.
In this section, 5 x 2-fold cross-validation strategy was conducted to evaluate the performance of the proposed method EURF [45, 46].
Ten methods were selected as candidates to test the performance of the proposed method EURF:
Table 3 shows that EURF performs the best AUC on 23 out of the 29 data sets and outperforms (is outperformed by) DTE_SBD, BC, EE, UBT, UBG, OBg, UC, OC, and RF on 26 (3), 29(0), 27(2), 29(0), 26(3), 28(1), 28(1), 29(0), 28(1), 27(2), and 27(2) out of the data sets.
From Table 7, EURF outperforms other methods on the comprehensive measures including AUC, g-mean, and f1-measure.
For the list of legal bases switching from unanimity to qualified majority (22 cases), the list of legal bases requiring unanimity (30) and the list of special cases requiring unanimity (21), see our EISNet site: www.eis.be => Advanced search => Reference = EURF;2785;100 .
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