Methods of multivariate analysis for imbalance data problem

N. Gagunashvili (UNAK & MPIK)

Under- and Oversampling TechniquesNikolai Gagunashvili (UNAK and MPIK)

Four possibilities that can be used for solving imbalance data problem

• Choice of appropriate classifier• Use cost sensitive approach• Use sampling based approach• Bagging

Main idea of sampling based approach is to modify the distribution of events so that the rare class is well represented in the training sample.

There are• Undersampling• Oversampling• Hybrid oversampling and undersampling

In case of undersampling we can take random sample of majority class (BG).

Potential problem : some of useful BG

instances may not be chosen for training and classifier will not be optimal.

Reduction majority class without losing performance of classification can be used

Class Number of instances in training sample

Number of instances in test sample

D0 1851

Background 496651 6704513

For illustration Monte-Carlo for D0 analysis will be used

Data is taken in mass window 1844.5GeV – 1884.5GeV

Algorithm of reduction number of background instances without losing performance

An instance t is removed if all k of its neighbors are of the same class. The instance is only removed, however, if its neighbors are at least 60% sure of their classification. For our example we take k = 20 then at least 12 instances should confirm the class of neighbors.

After reduction number of background combination reduced up to 19712 instances (more the 25 times lower sample)!

BG = 17861, D0 = 1851

Training sample: BG = 17861, D0 = 1851

Oversampling is replication the events of minority class.

Potential problem: could be for this method is overfitting for noisy data, because noisy data will be replicate.

To avoid overfitting the procedure of randomized

oversampling is proposed (SMOTE and Bordeline-SMOTE) with cleaning noisy data.

Hui Han, Wen-Yauan Wang, Bing-Huan Mao, Bodeline-SMOTE: A New Over-Sampling Method in Imbalanced Data Sets Learning, ICIC 2005, part 1, LNCS3644, 878-887, 2005.

Bodeline-SMOTE algorithm

Training sample: BG = 17861, D0 = 1851+3*555=3516

Cleaning procedure can improve performance of algorithms.

One of this procedure is removing instances that participate in Tomek links.

Tomek link is defined as a pair of instances x and y from different classes, that there exists no instances z such that d(x; z) < d(x; y) or d(y; z) < d(x; y), where d is the distance between a pair of examples.

Instances in Tomek links are noisy or lie in the decision border.

I. Tomek, Two Modifcations of CNN. IEEE Transactions on Systems Man and Communications SMC-6 (1976), 769-772.

Tr. sample: BG = 17861-456=17405, D0 = 3516-456=3060

Sizes of training samples

Class Training sample

After edition

After SMOTE

After Tomek link edition

D0 1851 1851 3516 3060

BG 496651 17861 17861 17405

Excluded attributes after wrapper:

Conclusions

Methods of undersampling related with filtering redundandant events of majority class permit improve performance of classifier essentially.

Oversampling with randomization (Bordeline SMOTE algorithm)

and removing events that participate in Tomek link improve performance of classifier.

Methods of multivariate analysis for imbalance data problem

Documents

N. Gagunashvili (UNAK & MPIK) Methods of multivariate analysis for imbalance data problem Under- and Oversampling Techniques Nikolai Gagunashvili (UNAK

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