The Kreȋn-SVM is a classification algorithm that is defined to incorporate a much broader class of kernel functions, known as indefinite kernel functions. Similarly to a standard kernel function, an indefinite kernel function implicitly maps instances into a new space. However, the space associated to an indefinite kernel function is known as a reproducing kernel Kreȋn Space (RKKS). Whilst operating in different spaces, the SVM and Kreȋn-SVM are conceptually similar. Both algorithms incorporate a kernel function, find the maximum-margin hyperplane in the associated space and are capable of learning non-linear decision surfaces.