Multi-prototype local density-based hierarchical clustering

In this paper, novel hierarchical clustering algorithms, Growing Fuzzy ART (GFA) and Self-Resonant Growing Fuzzy ART (SRGFA), based on connecting prototypes, are presented. The prototypes are generated by vector quantization algorithms: K-means, Self-Organizing Maps, and Fuzzy ART. The Euclidean distance is used to train the first two algorithms in order to allocate the centroids and neurons, respectively. The latter uses fuzzy set operations to check resonance and learn the categories. For each method, a subset of the data set is associated with each prototype; this subset consists of all patterns that, according to a similarity measure, are within a certain threshold from a given prototype. In the case of K-means and Self-Organizing Map, the region is a hypersphere, and in the case of Fuzzy ART, it is a hyperbox. In order to relax the similarity constraint and create larger subsets of data for each prototype, the values of the Euclidean norm and the vigilance parameter are continuously increased and decreased, respectively, according to a step size. Prototypes that have patterns in common are linked together in the process. The data set´s final partition is selected as the clustering state in which the algorithm spent most of its time. Synthetic and real world data sets are used to depict the experimental results. External validity indices are used as figures of merit to evaluate the quality of the final partitions.