Transitivity Clustering

Transitivity Clustering is based on the weighted transitive graph projection problem. A given similarity matrix is interpret as weighted graph and transformed into a so-called cost graph by removing edges weighted below a user-given threshold. Such a potentially intransitive graph is transformed into a transitive graph afterwards by adding and removing a minimal number of edges. Edge weights are taken into account by using a similarity-dependent cost function (the distance of the edge weight to the cutoff), which is to be minimized. A combination of exact and heuristic algorithms tackle this NP-hard problem. The number of clusters is influenced by the user threshold. The method guarantees that the mean similarity of objects within the same clusters is above the threshold, while the mean similarity between object from different clusters is below.