In this paper we propose a new approach in the development of kernel functions (kernels) for Support Vector Machines (SVMs) that could be applied in practical biomedicine as robust and sufficiently smooth classification and regression toolbox for cancer outcome prediction and diagnostic decision support commonly based on microarray, image and voice data. Recent major interest in biomedicine is connected with microarray data and its possible diagnostic and prognostic value. Nevertheless performed SVM classification frequently is based solely on kernels that represent very simple and well-known similarity concepts, i.e. inner products and their expansions to some higher dimensional Hilbert space. On the other hand topological expansion of frequently used RBF (Gaussian) and linear kernels is the main intent of this paper. Each gene or antigen “printed” on microarray chip could represent not only expression level but up- or down-regularity present in examined sample with respect to other involved (anti)genes. This information carefully rewritten could represent each sample topology and could serve as the topological expansion of every kernel. The experimental evaluations are performed on different biomedical datasets and verify that proposed kernel improves performance on purely conditioned and even very small training sets.