In this paper, we describe a novel kernel for multinomial distributions, namely the Quotient Basis Kernel (QBK), which is based on a suitable reparametrization of the input space through algebraic geometry and statistics. The QBK is used here for data transformation prior to classification in a medical problem concerning the prediction of mortality in patients suffering severe sepsis. This is a common clinical syndrome, often treated at the Intensive Care Unit (ICU) in a time-critical context. Mortality prediction results with Support Vector Machines using QBK compare favorably with those obtained using alternative kernels and standard clinical procedures.