Olli Virmajoki Pairwise Nearest Neighbor Method Revisited

The pairwise nearest neighbor (PNN) method, also known as Ward's method belongs to the class of agglomerative clustering methods. The PNN method generates hierarchical clustering using a sequence of merge operations until the desired number of clusters is obtained. This method selects the cluster pair to be merged so that it increases the given objective function value least. The main drawback of the PNN method is its slowness because the time complexity of the fastest known exact implementation of the PNN method is lower bounded by (N), where N is the number of data objects. We consider several speed-up methods for the PNN method in the first publication. These methods maintain the precision of the method. Another method for speeding-up the PNN method is investigated in the second publication, where we utilize a k-neighborhood graph for reducing distance calculations and operations. A remarkable speed-up is achieved at the cost of slight increase in distortion. The PNN method can also be adapted for multilevel thresholding, which can be seen as a 1-dimensional special case of the clustering problem. In the third publication, we show how this can be implemented efficiently using only O(N logN) time, in comparison to a straightforward approach that requires O(N). The merge philosophy is extended, by using the iterative shrinking method, in the fourth publication. In the merge phase of the PNN method, the two nearest clusters are always joined. Instead of this, we assign data objects to the neighboring clusters that they belong to. In this way, we get better clustering results; however, the results come at the cost of an increase in the running time. The proposed method is also used as a crossover method in a genetic algorithm, which produces the best clustering results in respect of the minimization of intra cluster variance. The PNN algorithm can also be applied to generating optimal clustering. In the fifth publication, we use a branch-and-bound technique for finding the best possible