{'fraction_non_alphanumeric': 0.016908212560386472, 'fraction_numerical': 0.001610305958132045, 'mean_word_length': 5.277777777777778, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A New Fuzzy Entropy Clustering Method with Controllable Membership Characteristics

Cluster analysis is a crucial and powerful tool for exploring and discovering the underlying structures in data. Among other approaches, the fuzzy c-means algorithm is the most well-known fuzzy clustering method. Recently, Tran and Wagner proposed a fuzzy entropy clustering method as an alternative to the fuzzy c-means. While the fuzzy c-means controls the degree of fuzziness and the membership function through the weighting exponent, the fuzzy entropy clustering method controls those by adjusting the ¿parameter. In this work, we present a modified form of Tran andWagner's method using a different definition of distance measure that is involved with the Euclidean distance and its higher-order terms. The proposed scheme adds more degrees of freedom in controlling the clustering results through two extra parameters, a1 and a2. We have explicitly derived the formulae for updating the fuzzy partition matrix and the cluster centers. A theoretical analysis on the resulting membership functions has also been carried out. Examples are given to demonstrate the clustering results of the presented scheme for different combinations of input parameters.