Rotation Forest: A New Classifier Ensemble Method 交通大學 電子所 蕭晴駿 Juan J. Rodríguez and Ludmila I. Kuncheva

2 Outline Introduction Rotation forests Experimental results Conclusions

3 Outline Introduction Rotation forests Experimental results Conclusions

4 Introduction(1) Why classifier ensemble? combine the predictions of multiple classifiers instead of single classifier Motivation - reduce variance: less dependent on peculiarities of a single training set - reduce bias: learn a more expressive concept class than a single classifier

5 Introduction(2) Key step: formation of an ensemble of diverse classifiers from a single training set It’s necessary to modify the data set (Bagging, Boosting) or the learning method (Random Forest) to create different classifiers Performance evaluation: diversity, accuracy

6 Bagging(1)

7 Bagging(2) Bootstrap sample - the individual classifiers have high classification accuracy - low diversity 1. for m = 1 to M // M... number of iterations a) draw (with replacement) a bootstrap sample S m of the data b) learn a classifier C m from S m 2. for each test example a) try all classifiers C m b) predict the class that receives the highest number of votes

8 Boosting Basic idea: - later classifiers focus on examples that were misclassified by earlier classifiers - weight the predictions of the classifiers with their error

9 Bagging vs. Boosting Making the classifiers diverse will reduce individual accuracy  accuracy-diversity dilemma AdaBoost creates inaccurate classifiers by forcing them to concentrate on difficult objects and ignore the rest of the data  large diversity that boost the ensemble performance

10 Outline Introduction Rotation forests Experimental results Conclusions

11 Rotation Forest(1) Rotation forest transforms the data set while preserving all information PCA is used to transform the data - subset of the instances - subset of the classes - subset of the features: low computation, low storage

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13 Rotation Forest(2) Base classifiers: decision tree  Forest PCA is a simple rotation of the coordinate axes  Rotation Forest

14 Method(1) X: the objects in the training data set x = [x 1, x 2, …, x n ] T a data point with n features N×n matrix Y = [y 1, y 2, …, y N ] T : class label with c classes

15 Method(2) Given: -L : the number of classifiers in the ensemble (D 1, D 2, …, D L ) -F : the feature set -X, Y All classifiers can be trained in parallel

16 Method(3) For i = 1 … L (to construct the training set for classifier D i ) F : feature set F i,1 F i,2 F i,3 … F i,K K subsets (F i,j j=1…K) each has M = n/K features

17 Method(3) For j = 1 … K F 1,1 F 1,2 F 1,3 … F 1,K X 1,1 : data set X for the features in F 1,1 Eliminate a random subset of classes Select a bootstrap sample from X 1,1 to obtain X’ 1,1 Run PCA on X’ 1,1 using only M features Principal components a (1) 1,1,…,a (M1) 1,1

18 Method(4) Arrange the principal components for all j to obtain rotation matrix Rearrange the rows of R 1 so as to match the order of features in F  obtain R 1 a Build classifier D 1 using XR 1 a as a training set

19 How It Works ? Diversity - Each decision tree uses different set of axes. - Trees are sensitive to rotation of the axes Accuracy - No principal components are discarded - The whole data set is used to train each classifier (with different extracted features)

20 Outline Introduction Rotation forests Experimental results Conclusions

21 Experimental Results(1) Experimental settings: 1. Bagging, AdaBoost, and Random Forest were kept at their default values in WEKA 2. for Rotation Forest, M is fixed to be 3 3. all ensemble methods have the same L 4. base classifier: tree classifier J48 (WEKA) 5. database: UCI Machine Learning Repository Waikato environment for knowledge analysis

22 Database

23 Experimental Results(2) TABLE 2 Classification Accuracy and Standard Deviation of J48 and Ensemble Methods without Pruning fold cross validation

24 Experimental Results(3) Fig. 1. Percentage diagram for the four studied ensemble methods with unpruned J48 trees. 3.03% % 3.03% 69.70%

25 Experimental Results (4) Fig. 2. Comparison of accuracy of Rotation Forest ensemble (RF) and the best accuracy from any of a single tree, Bagging, Boosting, and Random Forest ensembles.

26 Diversity-Error Diagram Pairwise diversity measures were chosen Kappa(κ) evaluates the level of agreement between two classifier outputs Diversity-error diagram - x-axis: κ for the pair - y-axis: averaged individual error of D i and D j E i,j =(E i +E j )/2 - small values of κ indicate the better diversity and small values of E i,j indicate better accuracy κ E i,j

27 Experimental Results (5) Rotation Forest has the potential to improve on diversity significantly without compromising the individual accuracy Fig. 3. Kappa-error diagrams for the vowel-n data set.

28 Experimental Results (6) Rotation Forest is not as diverse as the other ensembles but clearly has the most accurate classifiers Rotation Forest is similar to Bagging, but more accurate and diverse Fig. 4. Kappa-error diagrams for the waveform data set.

29 Conclusions Rotation Forest transforms the data with different axes while preserve the information completely  achieve diversity and accuracy Rotation Forest gives a scope for ensemble methods “on the side of Bagging”

30 References J.J. Rodriguez, L.I Kuncheva, and C.J. Alonso, “Rotation Forest: A New Classifier Ensemble Method,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp , Oct J.J. Rodriguez, C. J. Alonso, “Rotation-based ensembles,” Proc. Current Topics in Artificial Intelligence: 10th Conference of the Spanish Association for Artificial Intelligence, LNAI 3040, Springer, 2004, J. Furnkranz, “Ensemble Classifiers” (class notes)