Fuzzy Clustering Algorithm Based on Mahalanobis Distances with Recursive Process

Sue-Fen Huang ； Yuan-Horng Lin ； Jeng-Ming Yih ； Jui-Chiao Tseng

《International Journal of Intelligent Technologies and Applied Statistics》 10卷4期 (2017/12) Pp. 221-239

https://doi.org/10.6148/IJITAS.2017.1004.02

摘要

A fuzzy C-means algorithm based on Mahalanobis distance was proposed to improve those limitations of Gath-Geva (G-G) and Gustafson-Kessel (G-K) algorithms, but it is not stable enough when some of its covariance matrices are not equal. A new improved fuzzy C-means (FCM) algorithm based on a homogenous correlation matrix with Mahalanobis distance, which is called FCM-H. A fuzzy algorithm of FCM-H is proposed. Use the best performance of clustering algorithm FCM-H in data analysis and interpretation. G-K algorithm is an extension of the fuzzy C-means algorithm on an adaptive norm, which will provide information about the clusters of various shapes in a data set. However, the G-K algorithm can only be utilized for the clusters with the same volume in the data set. Both of G-K clustering algorithm and G-G clustering algorithm, based on semi-supervised Mahalanobis distance, these two algorithms fail to consider the relationships between cluster centers in the objective function. Hence, the algorithm will induce the singular problem for the inverse covariance matrix. A regulating factor of the covariance matrix for each class and the alternative global scatter matrix are added in the objective function, replaced all of the covariance matrices with the same common covariance matrix in the objective function based on Mahalanobis distance was proposed, which was extended by using the local and global Mahalanobis distance. Hence, the FCM based on Mahalanobis distances with recursive process iteratively can improve the stability of the clustering results, which will be called fuzzy clustering algorithm based on Mahalanobis distances with recursive process iteratively. In this paper, an improved supervised clustering algorithm based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the supervised clustering algorithm.

關鍵字

Mahalanobis distances ； FCM-NM ； G-K algorithm ； G-G algorithm