Performance of Distance Metrics in SMOTE for Binary Imbalanced Classification

Abstract

Skewed class distribution continues to be one of the central obstacles in binary classification, since a learning model tends to lean toward the dominant class and consequently overlooks observations belonging to the under-represented class. The purpose of this research is to examine how the choice of distance measure inside SMOTE, specifically Euclidean, Manhattan, Chebyshev, and Hamming, affects predictive quality on imbalanced binary data. Ten publicly available binary datasets drawn from the KEEL repository, whose imbalance ratios span from 1.86 up to 15.80, were used in the experiment. Every dataset was preprocessed and partitioned into 80% for training and 20% for testing; oversampling with SMOTE was carried out on the training portion only, after which four learners, namely Naive Bayes, Decision Tree, Logistic Regression, and k-Nearest Neighbor, were assessed. Model quality was judged through the Matthews Correlation Coefficient (MCC) together with the G-Mean, as these two indicators describe imbalanced performance more faithfully than plain accuracy. The comparison revealed that pairing Euclidean-based SMOTE with Logistic Regression yielded the strongest average scores (MCC = 0.72; G-Mean = 0.79); Manhattan-based SMOTE reached its top MCC again with Logistic Regression (MCC = 0.68) and its top G-Mean with the Decision Tree (G-Mean = 0.79); Chebyshev-based SMOTE delivered the best overall combination together with the Decision Tree (MCC = 0.74; G-Mean = 0.84); and Hamming-based SMOTE performed best alongside Logistic Regression (MCC = 0.73; G-Mean = 0.81). Taken together, these outcomes suggest that the distance function chosen within SMOTE shapes the quality of the generated synthetic points and, in turn, the behavior of the trained classifier.