Promote Clustering Accuracies With Fuzzy Supervised Clustering Algorithm

Huang-Shu Fen ； Jeng-Ming Yih

《International Journal of Intelligent Technologies and Applied Statistics》 14卷4期 (2021/12) Pp. 205-219

https://doi.org/10.6148/IJITAS.202112_14(4).0001

摘要

Purpose: Fuzzy algorithms of Gath-Geva (GG) and Gustafson-Kessel (GK) based on Mahalanobis distance can improve those limitations of spherical structural clusters, but GG algorithm can only be used for the data with multivariate normal distribution. GK algorithm is limited by that it must know the distribution of data. An improved supervised clustering algorithm based on fuzzy c-means (FCM) has been proposed. Methodology: We take a new threshold value and a new convergent algorithm to improve those limitations of GG and GK algorithms, delete the constraint of the determinants of covariance matrices in the GK algorithm, and replace the covariance matrix with the correlation matrix which exists in the objective function. Findings: The experimental results of real data sets show that our proposed new algorithm can promote clustering accuracies and get better performance. Value: The popular FCM algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Adding fuzzy covariance matrices in their distance measure was not directly derived from the objective function. But it is not stable enough when some of its covariance matrices are not equal. Hence, different initializations may lead to different results.

關鍵字

Fuzzy c-means algorithm ； Mahalanobis distance ； Spherical structural clusters ； Objective function