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

Sampriti Soor (1) , Aditya Challa (1) , Sravan Danda (1) , B S Daya Sagar (1) , Laurent Najman (2)

1 Systems Science and Informatics Unit
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

In digital age new approaches for effective and efficient governance strategies can be established by exploiting the vast computing and data resources at our disposal. In several cases, the problem of efficient governance translates to finding a solution to an optimization problem. A typical example is where several cases are framed in terms of clustering problem-Given a set of data objects, partition them into clusters such that elements belonging to the same cluster are similar and elements belonging to different clusters are dissimilar. For example, problems such as zonation, river linking, facility allocation and visualizing spatial data can all be framed as clustering problems. However, all these problems come with an additional constraint that the clusters must be connected. In this article, we propose a suitable solution to the clustering problem with a constraint that the clusters must be connected. 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. This algorithm is analyzed in detail using toy examples and the domain of image segmentation due to wide availability of labelled datasets. It has been shown that iterated watersheds perform 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 has been shown that iterated watersheds result in very good improvements over these methods across various experiments.

Mots clés: Graph Clustering; K-Means; E-governance; Watersheds

Domaines: Modélisation et simulation; Ingénierie assistée par ordinateur

Sampriti Soor, Aditya Challa, Sravan Danda, B S Daya Sagar, Laurent Najman. Iterated Watersheds, A Connected Variation of K-Means for Clustering GIS Data. IEEE Transactions on Emerging Topics in Computing, 2021, 9 (2), pp.626 - 636. ⟨10.1109/TETC.2019.2910147⟩. ⟨hal-02063210v2⟩