In the past few years, discriminative approaches to perform speaker detection have shown good results and an increasing interest. Among these methods, SVM based systems have lots of advantages, especially their ability to deal with a high dimension feature space. Generative systems such as UBMGMM systems show the greatest performance among other systems in speaker verification tasks. Combination of generative and discriminative approaches is not a new idea and has been studied several times by mapping a whole speech utterance onto a fixed length vector. This paper presents a straight-forward, cost friendly method to combine the two approaches with the use of a UBM model only to drive the experiment. We show that the use of the TFLLR kernel, while closely related to a reduced form of the Fisher mapping, implies a performance that is close to a standard GMM/UBM based speaker detection system. Moreover, we show that a combination of both outperforms the systems taken independently.