Fermat Clustering is a tool to compute clusters in data sets. It is based on Fermat distance, a method to compute distances between data points that captures the intrinsic structure of the data.
Most common clustering methods like K-means fail to compute clusters when they have a nonlinear geometry that is not captured by Euclidean distance.
By replacing Euclidean distance with Fermat distance you can use your favorite clustering algorithm with substantial improvement.
In this tutorial we cluster digits from MNIST data set with an algorithm as simple as K-means where Euclidean distance is replaced by Fermat distance.