Classic MEB (minimum enclosing ball) models characteristics of each class for classification by extracting core vectors through a (1 +
)-approximation problem solving. In this paper, we develop a new MEB system learning the core vectors set in a group manner, called group MEB (g-MEB). The g-MEB factorizes class characteristic in 3 aspects such as, reducing the sparseness in MEB by decomposing data space based on data distribution density, discriminating core vectors on class interaction hyperplanes, and enabling outliers detection to decrease noise affection. Experimental results show that the factorized core set from g-MEB delivers often apparently higher classification accuracies than the classic MEB.