Fast and accurate analysis of medical data is of great importance for diagnosis and treatment. In line with the technological developments, the size and diversity of these data have been increasing, which in turn makes their assessment difficult. Therefore, there is an ever growing need for automated decision support systems. To this end, clustering based applications are rapidly increasing in medicine thanks to their limited user interaction, no requirement of labeled training samples, and their effectiveness for decision and estimation. Among clustering methods, approximate spectral clustering (ASC), which depends on a pairwise similarity matrix of data points, has been recently popular and successful thanks to its ability to find irregularly shaped clusters and its independence from parametric cluster models. Various similarity criteria have been proposed to represent pairwise similarities. In this study, medical datasets have been analyzed by approximate spectral clustering with our geodesic distance based similarity criteria. Experimental results indicate that our approach performs better than traditional k-means and Euclidean based approximate spectral clustering.