Abstract: Recent researches have indicated that the standard minimum enclosing ball (MEB) can be used for training large datasets effectively by employing core vector machine (CVM). However, the generalized MEB can not be considered as the MEB problem due to its different constraint inequalities and accordingly we can not directly use CVM to train the generalized MEB for large datasets. In this paper, a fast learning approach called fast learning of generalized MEB (FL-GMEB) is presented for large datasets. First, FL-GMEB slightly relaxes the constraints in the generalized MEB such that it can be equivalent to the corresponding center-constrained MEB, which can be solved with the corresponding core set (CS) by CVM. Then, FL-GMEB attempts to obtain the extended core set (ECS) by expanding neighbors of some samples in CS into ECS in terms of the inverse concept of locally linear embedding (LLE). Finally, FL-GMEB takes the optimized weights of ECS as the approximate solution of the generalized MEB. Experimental results on UCI and USPS datasets demonstrate that the proposed method is effective.