Augmentation of Soft Partition with a Granular Prototype Based Fuzzy C-Means

Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft partition classification method which refines and extends the prototype of the well-known Fuzzy C-Means clustering algorithm. Specifically, the developed scheme employs membership function to extend the prototypes into a series of granular prototypes, thus achieving a deeper revelation of the structure of the data. This process softly divides the data into core and extended parts. The core part can be succinctly encapsulated through several information granules, whereas the extended part lacks discernible geometry and requires formal descriptors (such as membership formulas). Our objective is to develop information granules that shape the core structure within the dataset, delineate their characteristics, and explore the interaction among these granules that result in their deformation. The granular prototypes become the main component of the information granules and provide an optimization space for traditional prototypes. Subsequently, we apply quantum-behaved particle swarm optimization to identify the optimal partition matrix for the data. This optimized matrix significantly enhances the partition performance of the data. Experimental results provide substantial evidence of the effectiveness of the proposed approach.