An adaptive neighbor statistical ratio feature construction algorithm for Gaussian Naive Bayes classifier on imbalanced data

Gaussian Naive Bayes (GNB) classifiers face performance bottlenecks in imbalanced data. This bottleneck stems from two key issues: the estimation bias of minority class feature distribution and the weakened correlation between features and classes. To address this problem, this article proposes an Adaptive Neighbor Statistical Ratio (ANSR) feature construction algorithm. Different from sampling algorithms that tend to destroy distributions or lose information by merely adjusting sample sizes, and feature enhancement methods that are difficult to well adapt to the Gaussian assumption and lightweight requirements of GNB, this algorithm starts from the statistical correlation between features and classes, and constructs neighbor statistical ratio features of minority and majority classes to strengthen class differences. It focuses on the Gaussian distribution parameters relied on by GNB, maintains low-dimensional interpretability of features to adapt to its lightweight characteristics, and dynamically adjusts the number of neighbors based on the local density and boundary properties of samples to solve the estimation bias of statistics caused by fixed logic. Experimental results demonstrate that on 31 imbalanced datasets, ANSR generally achieves superior performance compared to 17 mainstream comparative algorithms in terms of area under curve (AUC), G-mean, and F-measure. Compared with the optimal value among comparative algorithms, the average performance improvements of ANSR reach 6.4% (AUC), 14.2% (G-mean), and 33.5% (F-measure) respectively. Especially in extreme imbalance scenarios and blurred boundary scenarios with severe sample overlap, ANSR achieves synchronous improvements in minority class recall and precision, which is conducive to effectively enhancing the classification performance of GNB classifiers.