Abstract
A support vector machine (SVM) plays a prominent role in classic machine learning, especially classification and regression. Through its structural risk minimization, it has enjoyed a good reputation in effectively reducing overfitting, avoiding dimensional disaster, and not falling into local minima. Nevertheless, existing SVMs do not perform well when facing class imbalance and large-scale samples. Undersampling is a plausible alternative to solve imbalanced problems in some way, but suffers from soaring computational complexity and reduced accuracy because of its enormous iterations and random sampling process. To improve their classification performance in dealing with data imbalance problems, this work proposes a weighted undersampling (WU) scheme for SVM based on space geometry distance, and thus produces an improved algorithm named WU-SVM. In WU-SVM, majority samples are grouped into some subregions (SRs) and assigned different weights according to their Euclidean distance to the hyper plane. The samples in an SR with higher weight have more chance to be sampled and put to use in each learning iteration, so as to retain the data distribution information of original data sets as much as possible. Comprehensive experiments are performed to test WU-SVM via 21 binary-class and six multiclass publically available data sets. The results show that it well outperforms the state-of-the-art methods in terms of three popular metrics for imbalanced classification, i.e., area under the curve, F-Measure, and G-Mean.