Fast and flexible unsupervised custering algorithm based on ultrametric properties

We introduce in this paper a competitive unsupervised clustering algorithm which has two strong features: it is fast and flexible on the processed data type as well as in terms of precision. Our approach has a computational cost, in the worst case, of O(n^2)+ ε, and in the average case, of O(n)+ ε. This complexity is due to the use of ultrametric distance properties. We create an ultrametric space from a sample data, chosen uniformly at random, in order to obtain a global view of proximities in the data set according to the similarity criterion. Then, we use this proximity profile to cluster the global set. We present two examples of our algorithm and compare our results with those of a classic clustering method.