Two novel fuzzy clustering methods for solving data clustering problems

In recent years, various data analysis techniques have been developed for extracting meaningful information from real-world data clustering problems. The results, running time, and clustering validity of the techniques are very important. During few decades, fuzzy clustering algorithms and especially the fuzzy c-means FCM algorithm has been widely utilized for solving data clustering problems. The fuzzy c-means algorithm FCM can perform well when applied to noise-free datasets, but performs somewhat poorly when applied to data that have been corrupted with noise, mainly because of the use of the non-robust objective function of FCM and the typical Euclidean distance measure of similarity or dissimilarity. To overcome these shortcomings, this work establishes effective objective functions of fuzzy c-means with the center learning method-based quadratic mean distance, entropy methods, and regularization terms. The effective membership function is derived and center updating by optimizing the proposed effective methods. This work introduces a center learning method to reduce the computational complexity and running time. Also, the proposed methods are applied to artificial data, checkerboard, and real-world datasets to evaluate their performance. The silhouette method is used to find the clustering accuracy of the proposed methods with those of other clustering methods. The experimental results reveal the advantages of the proposed clustering for application to real datasets and random data. They also reveal that the proposed methods outperform the other methods.