An efficient algorithm for computing the distance between close partitions Original Research Article

A image-partition of a set image is a splitting of image into image non-overlapping classes that cover all elements of image. Numerous practical applications dealing with data partitioning or clustering require computing the distance between two partitions. Previous articles proved that one can compute it in polynomial time—minimum image and maximum image—using a reduction to the linear assignment problem. We propose several conditions for which the partition distance can be computed in image time. In practical terms, this computation can be done in image time for any two relatively resembling partitions (i.e. with distance less than image) except specially constructed cases. Finally, we prove that, even if there is a bounded number of classes for which the proposed conditions are not satisfied, one can still preserve the linear complexity by exploiting decomposition properties of the similarity matrix.