MOSAIC: Agglomerative Clustering with Gabriel Graphs

Representative-based clustering algorithms are quite popular due to their relative high speed and because of their sound theoretical foundation. On the other hand, the clusters they can obtain are limited to convex shapes and clustering results are also highly sensitive to initializations. In this paper, a novel agglomerative clustering algorithm called MOSAIC is proposed which greedily merges neighboring clusters maximizing a given fitness function. MOSAIC uses Gabriel graphs to determine which clusters are neighboring and approximates non-convex shapes as the unions of small clusters that have been computed using a representative-based clustering algorithm. We evaluate MOSAIC for traditional unsupervised clustering with kmeans and DBSCAN, and also for supervised clustering. The experimental results show that this technique leads to clusters of higher quality compared to running a representative clustering algorithm stand-alone. Given a suitable fitness function, MOSAIC is able to detect arbitrary shape clusters which are comparable to the ones generated by DBSCAN. In addition, MOSAIC is capable of dealing with high dimensional data. We also claim that MOSAIC can be employed as an effective post-processing clustering algorithm to further improve the quality of clustering.