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A new methodology is proposed for clustering datasets in the presence of scattered observations. Scattered observations are defined as unlike any other, so traditional approaches that force them into groups can lead to erroneous conclusions. Our suggested approach is a scheme which, under assumption of homogeneous spherical clusters, iteratively builds cores around their centers and groups points within each core while identifying points outside as scatter. In the absence of scatter, the algorithm reduces to k-means. We also provide methodology to initialize the algorithm and to estimate the number of clusters in the dataset. Results in experimental situations show excellent performance, especially when clusters are elliptically symmetric. The methodology is applied to the analysis of the United States Environmental Protection Agency (EPA)’s Toxic Release Inventory (TRI) reports on industrial releases of mercury for the year 2000.

Improved statistical methods for k-means clustering of noisy and directional data