GenieOWA: Robustifying Hierarchical Clustering with OWAbased Linkages Abstract   We investigate the application of the Ordered Weighted Averaging (OWA) data fusion operator in agglomerative hierarchical clustering. The examined setting generalises the wellknown single, complete and average linkage schemes. It allows to embody expert knowledge in the cluster merge process and to provide a much wider range of possible linkages. We analyse various families of weighting functions on numerous benchmark data sets in order to assess their influence on the resulting cluster structure. Moreover, we inspect the correction for the inequality of cluster size distribution xe2x80x93 similar to the one in the Genie algorithm. Our results demonstrate that by robustifying the procedure with the Genie correction, we can obtain a significant performance boost in terms of clustering quality. This is particularly beneficial in the case of the linkages based on the closest distances between clusters, including the single linkage and its xe2x80x9csmoothedxe2x80x9d counterparts. To explain this behaviour, we propose a new linkage process called threestage OWA which yields further improvements. This way we confirm the intuition that hierarchical cluster analysis should rather take into account a few nearest neighbours of each point, instead of trying to adapt to their nonlocal neighbourhood.

Automatic Clustering by Detecting Significant Density Dips in Multiple Dimensions Clustering algorithms are used to find groups of similar items in a dataset. Automatic clustering algorithms achieve this task without requiring users to input critical parameters. A recent automatic clustering methodology uses Hartiganu0027s dip test to detect significant peaks in the distribution of a dataset. This test can detect peaks in the distribution of a onedimensional variable. To perform clustering in multiple dimensions, algorithms of this methodology rely on onedimensional transformations of the dataset, which limits their effectiveness. In this paper, we present MDip, an automatic clustering algorithm that works directly on multidimensional space. MDip also assumes that clusters correspond to different peaks in the distribution of the dataset. It separates clusters at the dips that form between neighboring peaks. Dips are detected directly in multidimensional space, using a graphbased method. Their statistical significance is evaluated through appropriate simulations. Our experimental evaluation indicates that MDip achieves significantly better results than existing algorithms based on Hartiganu0027s dip, as well as other stateoftheart automatic clustering algorithms.