Iterated Watersheds, A Connected Variation of K-Means for Clustering GIS Data

In this article, we propose a novel algorithm to obtain a solution to the clustering problem with an additional constraint of connectivity. This is achieved by suitably modifying K-Means algorithm to include connectivity constraints. The modified algorithm involves repeated application of watershed transform, and hence is referred to as iterated watersheds. Detailed analysis of the algorithm is performed using toy examples. Iterated watersheds is compared with several image segmentation algorithms. It has been shown that iterated watersheds performs better than methods such as spectral clustering, isoperimetric partitioning, and K-Means on various measures. To illustrate the applicability of iterated watersheds - a simple problem of placing emergency stations and suitable cost function is considered. Using real world road networks of various cities, iterated watersheds is compared with K-Means and greedy K-center methods. It is observed that iterated watersheds result in 4 - 66 percent improvement over K-Means and in 31 - 72 percent improvement over Greedy K-Centers in experiments on road networks of various cities.