Fuzzy Clustering Approaches Based on Numerical Optimizations of Modified Objective Functions - Erind Bedalli; Shkelqim Hajrulla; Rexhep Rada; Robert Kosova (Algorithms)
Fuzzy clustering is a form of unsupervised learning that assigns the elements of a dataset into multiple clusters with varying degrees of membership rather than assigning them to a single cluster. The classical Fuzzy C-Means algorithm operates as an iterative procedure that minimizes an objective function defined based on the weighted distance between each point and the cluster centers. The algorithm operates decently in many datasets but struggles with datasets that exhibit irregularities in overlapping shapes, densities, and sizes of clusters. Meanwhile, there is a growing demand for accurate and scalable clustering techniques, especially in high-dimensional data analysis. This research work aims to address these infirmities of the classical fuzzy clustering algorithm by applying several modification approaches on the objective function of this algorithm. These modifications include several regularization terms aiming to make the algorithm more robust in specific types of datasets. The optimization of the modified objective functions is handled based on several numerical methods: gradient descent, root mean square propagation (RMSprop), and adaptive mean estimation (Adam). These methods are implemented in a Python environment, and extensive experimental studies are conducted, following carefully the steps of dataset selection, algorithm implementation, hyper-parameter tuning, picking the evaluation metrics, and analyzing the results. A comparison of the features of these algorithms on various datasets is carefully summarized.