Augmentation of the reconstruction performance of Fuzzy C-Means with an optimized fuzzification factor vector

摘要

Information granules have been considered as the fundamental constructs of Granular Computing. As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation–degranulation mechanism plays a pivotal role in Granular Computing. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation–degranulation​ process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. Overall, we show that the enhanced version of the degranulation process is beneficial to reduce the deterioration of the reconstruction results and improve the performance of the mechanism of granulation–degranulation, which is also meaningful for transforming data between numeric form and granular format. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets demonstrate that the proposed approach outperforms the generic data reconstruction approach.