This thesis aims to apply the Dirichlet process mixture model to the cluster kernel framework. The probabilistic cluster kernel is extended with a Bayesian nonparametric model to avoid critical parameters within the model. The Dirichlet process cluster kernel demonstrate advantages compared to the probabilistic cluster kernel in both classification and clustering. Additionally, the two dimensional projection using kernel PCA and the Dirichlet process cluster kernel show compact clusters with a higher degree of cluster discrimination. The second main contribution of the thesis is an application of the cluster kernel methodology in semi-supervised learning. The Dirichlet process cluster kernel demonstrates a high degree of descriptive representation.