Bi-Fuzzy Clustering Algorithm by Augmented Granulation-Degranulation Mechanisms

We propose a method of bi-fuzzy clustering to enhance the classification performance of fuzzy clustering. In the proposed scheme, we first build a supervised learning mode of the granulation-degranulation mechanisms. Both the granulation and degranulation are considered as generalized rotation between the data subspace and the prototype subspace with the membership matrix. A rotational invariance form of the prototype subspace is derived with the supervised learning mode of the granulation-degranulation. The rotational invariance form of the prototype subspace implies that to improve the performance of the granulation-degranulation mechanisms is to diagonalize the rotation invariant matrix of the prototype subspace. Then, a joint diagonalization of the bi-generalized rotation matrices approach is derived by introducing a fuzzy coefficient increment. In other words, a clustering with double fuzzy coefficients can achieve better performance of fuzzy clustering. We offer a strict mathematical proof for the developed scheme. It is worth noting that the classical Fuzzy C-Means clustering algorithm is a special case of the proposed bi-fuzzy clustering. Comprehensive experimental studies involving publicly available datasets are reported to demonstrate the performance of the proposed bi-fuzzy clustering.