Hierarchical unsupervised fuzzy clustering

A recursive algorithm for hierarchical fuzzy partitioning is presented. The algorithm has the advantages of hierarchical clustering, while maintaining fuzzy clustering rules. Each pattern can have a nonzero membership in more than one subset of the data in the hierarchy. Optimal feature extraction and reduction is optionally reapplied for each subset. Combining hierarchical and fuzzy concepts is suggested as a natural feasible solution to the cluster validity problem of real data. The convergence and membership conservation of the algorithm are proven. The algorithm is shown to be effective for a variety of data sets with a wide dynamic range of both covariance matrices and number of members in each class.