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One of the popular tools in the exploratory phase of data mining and pattern recognition is the Kohonen Self Organizing Map (SOM). Recently, experiments have shown that to find the ambiguities involved in cluster analysis, it is not necessary to consider crisp boundaries in clustering operations. In this Book, the Incremental Leader algorithm for the thresholding of the SOM (Inc-SOM) is proposed to validate the potential of a crisp clustering algorithm. However, the performance deteriorates when there is overlap between clusters. To overcome the ambiguities in the results of cluster analysis, a rough thresholding for the SOM (Rough-SOM) is proposed. In Rough-SOM, the data is first trained by a SOM neural network, then the rough thresholding, which is a rough set based clustering approach, is applied on the neurons of the SOM. The optimal number of clusters can be found by rough set theory, which groups the neurons into a set of overlapping clusters. An optimization technique is applied during the last stage to assign the overlapped data to the true clusters.