In the paper, we first propose a new method to handle the problem of scoring a test utterance against a speaker model in the JFA Speaker Verification System, called Symmetric Scoring. The SS method is derived from the GMM log-likelihood-ratio approximation and is both symmetrical and efficient. Then we show that SS method and the JFA-SVM system using GMM super-vector space as input have nearly the same form in scoring phase. We also show that the performance of SS method is better than the JFA-SVM system, which indicates that applying the KL kernel function directly to obtain a score in GMM super-vector space is as effective as the JFA-SVM trained using the same kernel. As an inspiration of this direct scoring method in which kernel function is only used to calculate score without SVM training procedure, we try to extend the relationship to speaker factor space and evaluate some results based on different kernels.