Recently in [1], [2], a new kernel Fisher type contrast measure has been proposed to extract a target population in a data set contaminated by outliers. Although mathematically sound, this work presents some further shortcomings. First, the performance of the method relies on the assumption that the density between the target data and outliers is different. However, this consideration can easily prove to be over-optimistic for real world data sets making the method unreliable, at least directly. Secondly, this contrast measure is similar to a Generalized Rayleigh Quotient which is renowned for being sensitive to the small sample size problem. In this paper, we propose a null-space based version of their algorithm in order to unlock all these shortcomings and fully benefit from the interest of the approach. By this way, we show that the method can be used in a semi-supervised mode by considering that target objects can be beforehand collected and will serve as referentials to classify unseen objects. Experimental results on both synthetic and real data sets confirm the effectiveness of the proposed algorithm.