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In this paper, we present an agglomerative fuzzy K-Means clustering algorithm for numerical data, an extension to the standard fuzzy K-Means algorithm by introducing a penalty term to the objective function to make the clustering process not sensitive to the initial cluster centers. The new algorithm can produce more consistent clustering results from different sets of initial clusters centers. Combined with cluster validation techniques, the new algorithm can determine the number of clusters in a data set, which is a well-known problem in K-Means clustering. Experimental results on synthetic data sets (2 to 5 dimensions, 500 to 5,000 objects and 3 to 7 clusters), the BIRCH two-dimensional data set of 20,000 objects and 100 clusterOand the WINE data set of 178 objects, 17 dimensions, and 3 clusters from UCI have demonstrated the effectiveness of the new algorithm in producing consistent clustering results and determining the correct number of clusters in different data sets, some with overlapping inherent clusters. [ABSTRACT FROM AUTHOR]

In high-dimensional data, clusters can exist in subspaces that hide themselves from traditional clustering methods. A number of algorithms have been proposed to identify such projected clusters, but most of them rely on some user parameters to guide the clustering process. The clustering accuracy can be seriously degraded if incorrect values are used. Unfortunately, in real situations, it is rarely possible for users to supply the parameter values accurately, which causes practical difficulties in applying these algorithms to real data. In this paper, we analyze the major challenges of projected clustering and suggest why these algorithms need to depend heavily on user parameters. Based on the analysis, we propose a new algorithm that exploits the clustering status to adjust the internal thresholds dynamically without the assistance of user parameters. According to the results of extensive experiments on real and synthetic data, the new method has excellent accuracy and usability. It outperformed the other algorithms even when correct parameter values were artificially supplied to them. The encouraging results suggest that projected clustering can be a practical tool for various kinds of real applications. [ABSTRACT FROM AUTHOR]