Geodesic K-means clustering

We introduce a class of geodesic distances and extend the K-means clustering algorithm to employ this distance metric. Empirically, we demonstrate that our geodesic K-means algorithm exhibits several desirable characteristics missing in the classical K-means. These include adjusting to varying densities of clusters, high levels of resistance to outliers, and handling clusters that are not linearly separable. Furthermore our comparative experiments show that geodesic K-means comes very close to competing with state-of-the-art algorithms such as spectral and hierarchical clustering.