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. The experimental results show that this technique leads to clusters of higher quality compared to running a representative clustering algorithm standalone. Given a suitable fitness function, MOSAIC is able to detect arbitrary shape clusters. In addition, MOSAIC is capable of dealing with high dimensional data.

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Abstract. Existing data mining techniques mostly focus on finding global patterns and lack the ability to systematically discover regional patterns. Most relationships in spatial datasets are regional; therefore there is a great need to extract regional knowledge from spatial datasets. This paper proposes a novel framework to discover interesting regions characterized by "strong regional correlation relationships" between attributes, and methods to analyze differences and similarities between regions. The framework employs a twophase approach: it first discovers regions by employing clustering algorithms that maximize a PCA-based fitness function and then applies post processing techniques to explain underlying regional structures and correlation patterns. Additionally, a new similarity measure that assesses the structural similarity of regions based on correlation sets is introduced. We evaluate our framework in a case study which centers on finding correlations between arsenic pollution and other factors in water wells and demonstrate that our framework effectively identifies regional correlation patterns.

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Strong theoretical foundation and low computational complexity make representative-based clustering one of the most popular approaches for a clustering problem. Despite those superiorities, it presents two main drawbacks: the shape of clusters obtained is limited to convex shapes, and its performance is highly dependent on seeds initialization. To address these problems, the authors introduce MOSAIC, a novel agglomerative clustering algorithm, which greedily merges neighboring clusters maximizing a plug-in fitness function. The key idea is that by considering neighboring relationship computed using Gabriel Graphs among cluster, MOSAIC can derive non-convex shapes as the unions of small clusters previously generated by a representative-based clustering algorithm. The authors evaluate MOSAIC for traditional unsupervised clustering with k-means and DBSCAN, and also for supervised clustering. The experimental results show that compared to k-means stand-alone, their proposed post-processing techniques obtain higher quality clusters, whereas compared to DBSCAN results, MOSAIC is capable of identifying comparable arbitrary shape clusters, given a suitable fitness function. In addition, MOSAIC can cope with problems of clustering on high dimensional data. The authors also claim that MOSAIC can be employed as an effective post-processing clustering algorithm to further improve the quality of clustering.