The analysis of single-cell RNA sequencing data is of great importance in health research. It challenges data scientists, but has enormous potential in the context of personalized medicine. The clustering of single cells aims to detect different subgroups of cell populations within a patient in a data-driven manner. Some comparison studies denote single-cell consensus clustering (SC3), proposed by Kiselev et al. (Nat Methods 14(5):483–486, 2017), as the best method for classifying single-cell RNA sequencing data. SC3 includes Laplacian eigenmaps and a principal component analysis (PCA). Our proposal of unsupervised adapted single-cell consensus clustering (adaSC3) suggests to replace the linear PCA by diffusion maps, a non-linear method that takes the transition of single cells into account. We investigate the performance of adaSC3 in terms of accuracy on the data sets of the original source of SC3 as well as in a simulation study. A comparison of adaSC3 with SC3 as well as with related algorithms based on further alternative dimension reduction techniques shows a quite convincing behavior of adaSC3.