Geometric Structural Ensemble Learning for Imbalanced Problems.

The classification on imbalanced data sets is a great challenge in machine learning. In this paper, a geometric structural ensemble (GSE) learning framework is proposed to address the issue. It is known that the traditional ensemble methods train and combine a series of basic classifiers according to various weights, which might lack the geometric meaning. Oppositely, the GSE partitions and eliminates redundant majority samples by generating hyper-sphere through the Euclidean metric and learns basic classifiers to enclose the minority samples, which achieves higher efficiency in the training process and seems easier to understand. In detail, the current weak classifier builds boundaries between the majority and the minority samples and removes the former. Then, the remaining samples are used to train the next. When the training process is done, all of the majority samples could be cleaned and the combination of all basic classifiers is obtained. To further improve the generalization, two relaxation techniques are proposed. Theoretically, the computational complexity of GSE could approach O(ndlog(nmin)log(n maj)) . The comprehensive experiments validate both the effectiveness and efficiency of GSE.