For the cross-space affinity learning problem, the recently-proposed cross-space affinity learng(CSAL) algorithm exhibits its good performance, and successfully applies to various recommendation systems. The data of a perfect recommendation system often have characteristics of large scale sample, but the CSAL algorithm does not have the capacity of fast processing big data. To solve this problem, the cross-space affinity learng-minimal enclosing ball(CSAL-MEB) method and cross-space affinity learng-core vector machine(CSAL-CVM) method are proposed. The CSAL-CVM method has the merits of asymmetric time complexity and space requirements independent of data scale as well as inherits the good performance of the CSAL algorithm. Experiments are given to verify the effectiveness of the proposed method.