Modeling and Clustering of Parabolic Granular Data

At present, there exist some problems in granular clustering methods, such as lack of nonlinear membership description and global optimization of granular data boundaries. To address these issues, in this study, revolving around the parabolic granular data, we propose an overall architecture for parabolic granular modeling and clustering. To begin with, novel coverage and specificity functions are established, and then a parabolic granular data structure is proposed. The fuzzy c-means (FCM) algorithm is used to obtain the numeric prototypes, and then particle swarm optimization (PSO) is introduced to construct the parabolic granular data from the global perspective under the guidance of principle of justifiable granularity (PJG). Combining the advantages of FCM and PSO, we propose the parabolic granular modeling and optimization (PGMO) method. Moreover, we put forward attribute weights and sample weights as well as a distance measure induced by the Gaussian kernel similarity, and then come up with the algorithm of weighted kernel fuzzy clustering for parabolic granularity (WKFC-PG). In addition, the assessment mechanism of parabolic granular clustering is discussed. In summary, we set up an overall architecture including parabolic granular modeling, clustering, and assessment. Finally, comparative experiments on artificial, UCI, and high-dimensional datasets validate that our overall architecture delivers a good improvement over previous strategies. The parameter analysis and time complexity are also given for WKFC-PG. In contrast with related granular clustering algorithms, it is observed that WKFC-PG performs better than other granular clustering algorithms and has superior stability in handling outliers, especially on high-dimensional datasets.