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Why Does Rebalancing Class-Unbalanced Data Improve AUC for Linear Discriminant Analysis?

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IEEE Transactions on Pattern Analysis and Machine Intelligence

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Area of Science:

Machine Learning
Statistical Classification

Background:

Class imbalance is a common challenge in machine learning, where classifiers struggle with minority class detection.
Current methods often involve rebalancing training data via oversampling or undersampling to improve performance.

Purpose of the Study:

To provide a theoretical explanation for the observed empirical improvement in Area Under the Curve (AUC) after class rebalancing.
To investigate the relationship between class rebalancing and AUC improvement in classification tasks.

Main Methods:

Utilized Gaussian-based Linear Discriminant Analysis (LDA) as the classification model.
Analyzed the theoretical relationship between training data class size rebalancing and AUC on original, unbalanced test data.

Main Results:

Demonstrated an intrinsic, positive relationship between class rebalancing and AUC improvement for LDA.
Showed that maximum AUC improvement is asymptotically achieved when classes are rebalanced to be of equal sizes.

Conclusions:

Class rebalancing, especially towards equal distribution, offers a theoretically sound method to enhance AUC in LDA classifiers.
The findings provide a foundational understanding for addressing class imbalance in classification problems.