The problem of outlier detection consists in finding data that is not representative of the population from which it was ostensibly derived. Recently, to solve this problem, Liu et al. [1] proposed a two steps hypersphere-based approach, taking into account a confidence score pre-calculated for each input data. Defining these scores in a first step, independently from the second one, makes this approach not well-suited for large stream data. To solve these difficulties, we propose a global reformulation of the support vector data description (SVDD) problem based on the L0 norm, well suited for outlier detection. We demonstrate that this L0-SVDD problem can be solved using an iterative procedure providing data specific weighting terms. We show that our approach outperforms state of the art outlier detection techniques using both synthetic and clinical data.